decompwlj 3D

Digit rule · 306 sequences

The sequences of the family “digit rule”, by A-number, with the share of their decomposable terms in the level class (k > L).

A-numberNameLevel
A000787Strobogrammatic numbers: the same upside down93.4 %
A000966n! never ends in this many 0's19.4 %
A001101Moran numbers: k such that k/(sum of digits of k) is prime35.6 %
A001363Primes in ternary27.9 %
A001633Numbers with an odd number of digits9.2 %
A001637Numbers with an even number of digits8.7 %
A001704a(n) = n concatenated with n + 1100.0 %
A001729List of numbers whose digits contain no loops (version 1)15.0 %
A001740Squares written in base 5100.0 %
A001741Squares written in base 6100.0 %
A001742Numbers whose digits contain no loops (version 2)17.1 %
A001743Numbers in which every digit contains at least one loop (version 1)13.5 %
A001744Numbers n such that every digit contains a loop (version 2)13.7 %
A001745Numbers such that at least one digit contains a loop (version 2). Also called "holey" or "holy" numbers9.8 %
A001746At least one digit contains a loop (version 1)9.9 %
A002113Palindromes in base 1071.7 %
A002440Squares written in base 7100.0 %
A002441Squares written in base 8100.0 %
A002442Squares written in base 9100.0 %
A002796Numbers that are divisible by each nonzero digit13.9 %
A003052Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m)24.9 %
A003219Self numbers divisible by sum of their digits (or, self numbers which are also Harshad numbers)33.2 %
A003278Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), k0.4 %
A003635Inconsummate numbers in base 10: no number is this multiple of the sum of its digits (in base 10)18.0 %
A004207a(0) = 1, a(n) = sum of digits of all previous terms14.2 %
A004678Primes written in base 427.3 %
A004679Primes written in base 527.6 %
A004680Primes written in base 630.7 %
A004681Primes written in base 723.6 %
A004682Primes written in base 830.8 %
A004683Primes written in base 924.6 %
A005349Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits20.3 %
A005836Numbers whose base-3 representation contains no 214.7 %
A006507a(n+1) = a(n) + sum of digits of a(n), with a(1)=714.2 %
A006753Smith (or joke) numbers: composite numbers k such that sum of digits of k = sum of digits of prime factors of k (counted with multiplicity)29.2 %
A007089Numbers in base 310.7 %
A007090Numbers in base 412.7 %
A007091Numbers in base 511.1 %
A007092Numbers in base 610.6 %
A007093Numbers in base 711.8 %
A007094Numbers in base 810.0 %
A007095Numbers in base 99.2 %
A007612a(n+1) = a(n) + digital root (A010888) of a(n)0.0 %
A007618a(n) = a(n-1) + sum of digits of a(n-1), a(1) = 514.2 %
A007770Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 119.7 %
A007928Numbers containing an even digit9.3 %
A007931Numbers that contain only 1's and 2's. Nonempty binary strings of length n in lexicographic order11.1 %
A007932Numbers that contain only 1's, 2's and 3's10.7 %
A007957Numbers that contain an odd digit9.9 %
A009440a(n) is the concatenation of n and 6n100.0 %
A009441a(n) is the concatenation of n and 7n100.0 %
A009470a(n) is the concatenation of n and 8n100.0 %
A009474a(n) is the concatenation of n and 9n100.0 %
A009994Numbers with digits in nondecreasing order19.8 %
A009996Numbers with digits in nonincreasing order17.2 %
A010062a(0)=1; thereafter a(n+1) = a(n) + number of 1's in binary representation of a(n)23.9 %
A010063a(n+1) = a(n) + sum of digits in base 3 representation of a(n), with a(0) = 122.3 %
A010064Base 4 self or Colombian numbers (not of form k + sum of base 4 digits of k)19.2 %
A010065a(n+1) = a(n) + sum of digits in base 4 representation of a(n), with a(0) = 118.3 %
A010066a(n+1) = a(n) + sum of digits in base 5 representation of a(n)19.9 %
A010067Base 6 self or Colombian numbers (not of form k + sum of base 6 digits of k)20.8 %
A010068a(n+1) = a(n) + sum of digits in base 6 representation of a(n)16.9 %
A010069a(n+1) = a(n) + sum of digits in base 7 representation of a(n)15.9 %
A010070Base 8 self or Colombian numbers (not of form k + sum of base 8 digits of k)22.9 %
A010071a(n+1) = a(n) + sum of digits in base 8 representation of a(n)15.9 %
A010072a(n+1) = a(n) + sum of digits in base 9 representation of a(n)17.8 %
A011531Numbers that contain a digit 1 in their decimal representation11.1 %
A011532Numbers that contain a 211.4 %
A011533Numbers that contain a 312.7 %
A011534Numbers that contain a 411.5 %
A011535Numbers that contain a 510.8 %
A011536Numbers that contain a 612.0 %
A011537Numbers that contain at least one 713.6 %
A011538Numbers that contain an 811.2 %
A011539"9ish numbers": decimal representation contains at least one nine13.6 %
A011540Numbers that contain a digit 08.8 %
A014190Palindromes in base 3 (written in base 10)84.2 %
A014192Palindromes in base 4 (written in base 10)83.2 %
A014261Numbers that contain odd digits only17.4 %
A014263Numbers that contain even digits only11.1 %
A015976One iteration of Reverse and Add is needed to reach a palindrome10.7 %
A015977Two iterations of Reverse and Add are needed to reach a palindrome13.0 %
A015979Three iterations of Reverse and Add are needed to reach a palindrome16.2 %
A015980Four iterations of Reverse and Add are needed to reach a palindrome20.4 %
A015982Five iterations of Reverse and Add are needed to reach a palindrome21.0 %
A015984Six iterations of Reverse and Add are needed to reach a palindrome23.8 %
A016038Strictly non-palindromic numbers: n is not palindromic in any base b with 2 <= b <= n-243.1 %
A016052a(1) = 3; for n >= 1, a(n+1) = a(n) + sum of its digits14.7 %
A016096a(n+1) = a(n) + sum of its digits, with a(1) = 917.4 %
A019506Hoax numbers: composite numbers whose digit-sum equals the sum of the digit-sums of its distinct prime factors27.5 %
A019550a(n) is the concatenation of n and 2n100.0 %
A019551a(n) is the concatenation of n and 3n100.0 %
A019552a(n) is the concatenation of n and 4n100.0 %
A019553a(n) is the concatenation of n and 5n100.0 %
A020899Numbers k with an odd number of terms in their Zeckendorf representation (write k as a sum of non-consecutive distinct Fibonacci numbers)13.0 %
A023692Numbers with a single 1 in their ternary expansion23.5 %
A023699Numbers with a single 2 in their ternary expansion16.8 %
A023705Numbers with no 0's in base-4 expansion12.2 %
A023706Numbers with a single 0 in their base 4 expansion12.5 %
A023709Numbers with no 1's in their base 4 expansion13.8 %
A023710Numbers with a single 1 in their base 4 expansion15.9 %
A023713Numbers with no 2's in their base 4 expansion14.2 %
A023714Numbers with a single 2 in their base 4 expansion13.9 %
A023717Numbers with no 3's in base-4 expansion7.8 %
A023718Numbers with a single 3 in their base 4 expansion9.9 %
A023721Numbers with no 0's in their base-5 expansion10.3 %
A023722Numbers with a single 0 in their base 5 expansion10.6 %
A023725Numbers with no 1's in their base-5 expansion13.0 %
A023726Numbers with a single 1 in their base 5 expansion15.1 %
A023729Numbers with no 2's in their base-5 expansion13.3 %
A023730Numbers with a single 2 in their base 5 expansion15.0 %
A023733Numbers with no 3's in base-5 expansion6.9 %
A023734Numbers with a single 3 in their base-5 expansion8.1 %
A023738Numbers with a single 4 in their base 5 expansion12.4 %
A028373Numbers that have only the straight digits {1, 4, 7}18.0 %
A028374Numbers that have only curved digits {0, 3, 6, 8, 9} or digits that are both curved and linear {2, 5}13.9 %
A028834Numbers whose sum of digits is a prime10.7 %
A028835Numbers whose iterated sum of digits is a prime12.2 %
A028838Numbers whose sum of digits is a power of 227.0 %
A028839Sum of digits of n is a square25.2 %
A028840Numbers k such that sum of digits of k is a Fibonacci number24.0 %
A028846Numbers whose product of digits is a power of 25.2 %
A029581Numbers in which all digits are composite13.7 %
A029730Numbers that are palindromic in base 1676.2 %
A029742Nonpalindromic numbers9.6 %
A029803Numbers that are palindromic in base 884.9 %
A029952Palindromic in base 578.4 %
A029953Palindromic in base 683.2 %
A029954Palindromic in base 777.1 %
A029955Palindromic in base 979.6 %
A029956Numbers that are palindromic in base 1175.4 %
A029957Numbers that are palindromic in base 1279.5 %
A029958Numbers that are palindromic in base 1380.8 %
A029959Numbers that are palindromic in base 1483.4 %
A029960Numbers that are palindromic in base 1580.0 %
A030141Numbers in which parity of the decimal digits alternates14.3 %
A030143Even numbers in which parity of digits alternates9.6 %
A030457Numbers k such that k concatenated with k+1 is prime26.2 %
A031177Unhappy numbers: numbers having period-8 2-digitized sequences10.4 %
A031955Numbers with exactly two distinct base-10 digits22.9 %
A032810Numbers using only digits 2 and 312.4 %
A032822Numbers whose set of base-10 digits is {1,4}14.7 %
A032834Numbers with digits 3 and 4 only6.3 %
A032917Numbers having only digits 1 and 3 in their decimal representation14.0 %
A032924Numbers whose ternary expansion contains no 04.9 %
A032981Positive numbers with the property that all pairs of consecutive base-10 digits differ by 0 or 111.7 %
A033298a(n+1) = a(n) + sum of digits of a(n)^2, with a(1) = 132.1 %
A034048Numbers with multiplicative digital root value 010.2 %
A034709Numbers divisible by their last digit15.2 %
A034837Numbers that are divisible by the first, i.e., the leftmost, digit9.2 %
A034838Numbers k that are divisible by every digit of k14.7 %
A035333Concatenation of two or more consecutive positive integers99.9 %
A036301Numbers whose sum of even digits and sum of odd digits are equal28.8 %
A036435Digits are nonzero squares18.1 %
A037301Numbers whose base-2 and base-3 expansions have the same digit sum17.9 %
A037308Numbers whose base-2 and base-10 expansions have the same digit sum21.3 %
A037372Positive numbers k such that every base-2 digit of k is a base-3 digit of k9.5 %
A037373Positive numbers k such that every base-2 digit of k is a base-4 digit of k9.7 %
A037374Positive numbers k such that every base-2 digit of k is a base-5 digit of k10.0 %
A037380Numbers whose base-3 digits are all present among their base-4 digits9.7 %
A037386Every base 3 digit of n is a base 10 digit of n14.1 %
A038366n is divisible by (product of digits) + (sum of digits)19.4 %
A038367Numbers n with property that (product of digits of n) is divisible by (sum of digits of n)11.8 %
A038368n is divisible by |(product of digits) - (sum of digits)|19.5 %
A038770Numbers divisible by at least one of their digits11.1 %
A038772Numbers not divisible by any of their digits10.9 %
A039004Numbers whose base-4 representation has the same number of 1's and 2's10.8 %
A043096Numbers in which every pair of adjacent digits are distinct9.7 %
A043489Numbers having one 0 in base 109.9 %
A043493Numbers that contain a single 111.3 %
A045926All digits even and nonzero11.2 %
A046030Numbers whose digits are squares15.6 %
A046031Digits are cubes15.8 %
A046034Numbers whose digits are primes17.3 %
A046758Equidigital numbers16.2 %
A046759Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n)41.2 %
A046760Wasteful numbers11.5 %
A047791Numbers n such that n plus digit sum of n (A007953) equals a prime19.9 %
A050695Composite numbers k such that none of the prime factors of k is a substring of k14.1 %
A050813Numbers n not palindromic in any base b, 2 <= b <= 109.8 %
A051004Numbers divisible both by their individual digits and by the sum of their digits19.3 %
A052018Numbers k with the property that the sum of the digits of k is a substring of k20.5 %
A052026Composites base 10 that remain composite in all bases b, 2<=b<=10, expansions interpreted as decimal numbers11.6 %
A052040Numbers whose square is zeroless12.2 %
A052044Numbers k such that k^3 lacks the digit zero in its decimal expansion15.7 %
A052223Numbers whose sum of digits is 913.0 %
A052382Numbers without 0 in the decimal expansion, colloquial 'zeroless numbers'10.5 %
A052383Numbers without 1 as a digit9.3 %
A052404Numbers without 2 as a digit10.4 %
A052405Numbers without 3 as a digit8.1 %
A052406Numbers without 4 as a digit10.5 %
A052413Numbers without 5 as a digit9.6 %
A052414Numbers without 6 as a digit13.1 %
A052419Numbers without 7 as a digit11.9 %
A052421Numbers without 8 as a digit8.0 %
A053432Numbers with digits in alphabetical order (in English)15.7 %
A054211Numbers k such that k concatenated with k-1 is prime26.3 %
A054683Numbers whose sum of digits is even10.1 %
A054684Numbers whose sum of digits is odd11.0 %
A056524Palindromes with even number of digits94.5 %
A057104The non-octal numbers: numbers containing an 8 or 9 (they cannot be mistaken for octal numbers)9.5 %
A057436Contains digits 1 through 6 only11.5 %
A058369Numbers k such that k and k^2 have same digit sum33.8 %
A059094Numbers whose sum of digits is a cube11.1 %
A059708Numbers k such that all digits have same parity15.5 %
A060874Intrinsic 4-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base29.2 %
A060879Intrinsic 9-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base59.9 %
A060947Intrinsic 10-palindromes: n is an intrinsic k-palindrome if it is a k-digit palindrome in some base82.3 %
A061384Numbers n such that sum of digits = number of digits23.8 %
A061426Geometric mean of the digits = 2. In other words, the product of the digits is = 2^k where k is the number of digits26.9 %
A062713Numbers k such that the sum of the digits of k is a prime factor of k33.5 %
A062996Numbers whose sum of digits is greater than or equal to its product of digits8.9 %
A062997Numbers whose sum of digits is strictly greater than its product of digits8.9 %
A062998Numbers whose sum of digits is less than or equal to its product of digits10.5 %
A064150Numbers divisible by the sum of their ternary digits19.7 %
A064481Numbers which are divisible by the sum of their base-5 digits18.6 %
A064700Numbers k that are divisible by the multiplicative digital root of k20.7 %
A065877Non-Niven (or non-Harshad) numbers: numbers which are not a multiple of the sum of their digits8.3 %
A070938Harshad numbers which terminate in their digital sum25.3 %
A072960Numbers using only the curved digits 0, 3, 6, 8 and 913.0 %
A072961Numbers using only the digits 2 and 5, that are both curved and straight15.2 %
A074940Numbers having at least one 2 in their ternary representation9.7 %
A079498Numbers whose sum of digits in base b gives 0 (mod b), for b = 316.2 %
A080228Numbers containing the digits 0, 1, 2, 5 or 8 only14.6 %
A081605Numbers having at least one 0 in their ternary representation9.6 %
A084544Alternate number system in base 411.2 %
A084545Alternate number system in base 512.9 %
A084984Numbers containing no prime digits15.2 %
A085370Niven (or Harshad) numbers that are not divisible by 323.6 %
A085371Non-Niven (or non-Harshad) numbers that are divisible by 38.3 %
A085802Numbers whose sum of digits is a semiprime13.7 %
A092620Numbers with exactly one prime digit16.5 %
A094677Sum of digits is divisible by 1024.6 %
A095050Numbers such that all ten digits are needed to write all positive divisors in decimal representation14.3 %
A101594Numbers with exactly two distinct decimal digits, neither of which is 022.6 %
A101813Odd Niven (or Harshad) numbers: odd numbers that are divisible by the sum of their digits33.9 %
A101814Even Niven (or Harshad) numbers: even numbers that are divisible by the sum of their digits18.8 %
A102487Numbers in base-12 representation that can be written with decimal digits11.1 %
A102491Numbers whose base-20 representation can be written with decimal digits10.9 %
A106039Belgian-0 numbers16.7 %
A106439Belgian-1 numbers17.9 %
A106518Belgian-2 numbers15.7 %
A106596Belgian-3 numbers17.5 %
A107665Numbers with semiprime digits (digits 4, 6, 9 only)16.2 %
A109303Numbers k with at least one duplicate base-10 digit (A107846(k) > 0)10.7 %
A117804Natural position of n in the string 12345678910111213...10.7 %
A118363Factorial base Niven (or Harshad) numbers: numbers that are divisible by the sum of their factorial base digits22.4 %
A118950Numbers containing at least one prime digit10.2 %
A118951Numbers containing at least one composite digit9.9 %
A119735Numbers n such that every digit occurs at least once in n^320.2 %
A121022Even numbers containing a 2 in their decimal representation11.5 %
A121030Multiples of 10 containing a 10 in their decimal representation24.3 %
A121032Multiples of 12 containing a 12 in their decimal representation19.6 %
A129845Numbers n such that n and 2n share at least one digit9.8 %
A131835Numbers starting with 18.7 %
A132359Numbers divisible by the square of their last decimal digit22.0 %
A134027Nonnegative numbers that are palindromes in balanced ternary representation93.8 %
A136333Numbers containing only digits coprime to 10 in their decimal representation17.5 %
A143164Numbers with digitsum 13, in increasing order30.9 %
A143967Numbers containing only digits 3 or 7 in decimal representation18.0 %
A154314Numbers with not more than two distinct digits in ternary representation11.4 %
A158704Nonnegative integers with an even number of even powers of 2 in their base-2 representation15.3 %
A158705Nonnegative integers with an odd number of even powers of 2 in their base-2 representation15.0 %
A168501Numbers without the decimal digits 2, 4 and 616.1 %
A174813a(n) = number whose product of digits equals a power of 320.4 %
A176995Numbers that can be written as (m + sum of digits of m) for some m10.0 %
A178361Numbers with rounded up arithmetic mean of digits = 113.8 %
A178403Numbers containing the rounded up arithmetic mean of their digits at least once, cf. A00442711.7 %
A179244Numbers that have 4 terms in their Zeckendorf representation27.9 %
A182175Numbers with the property that every pair of adjacent digits sum to a prime number14.5 %
A202267Numbers in which all digits are noncomposites (1, 2, 3, 5, 7) or 015.7 %
A202268Numbers in which all digits are neither primes nor zero, i.e., are members of (1, 4, 6, 8, 9)15.8 %
A214423Numbers k palindromic in only one base b, 2 <= b <= 1042.4 %
A214584Integers whose decimal representation has only digits in {4,5,7}11.0 %
A227793Numbers whose digital sum is a multiple of 520.3 %
A230633Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly one solution11.7 %
A230634Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly two solutions18.1 %
A230853Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly one solution20.3 %
A230854Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly two solutions11.3 %
A233010In balanced ternary notation, either a palindrome or becomes a palindrome if trailing 0's are omitted68.9 %
A256290Numbers which have only digits 4 and 5 in base 1012.4 %
A256291Numbers which have only digits 5 and 6 in base 1010.7 %
A256292Numbers which have only digits 6 and 7 in base 108.6 %
A256340Numbers which have only digits 7 and 8 in base 1010.0 %
A256601Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 9 as largest digit20.2 %
A256634Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digit22.2 %
A257210Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 7 as largest digit34.4 %
A257211Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digit24.2 %
A257368Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digit31.2 %
A268620Numbers whose digital sum is a multiple of 420.2 %
A273159Numbers whose digit sum is divisible by 723.2 %
A273188Numbers whose digit sum is divisible by 824.8 %
A274319Numbers whose digit sum is divisible by 69.0 %
A276037Numbers using only digits 1 and 518.4 %
A276039Numbers using only digits 1 and 717.2 %
A276137Numbers without the decimal digits 2, 4, 6 and 815.5 %
A276138Numbers without the decimal digits 1, 3, 5 and 712.9 %
A284293Numbers using only digits 1 and 616.5 %
A284379Numbers k with digits 3 and 5 only15.7 %
A284380Numbers k with digits 5 and 7 only15.3 %
A284381Numbers k with digits 5 and 8 only14.2 %
A284632Numbers n with digits 2 and 6 only14.0 %
A284633Numbers n with digits 3 and 6 only11.1 %
A307913Numbers without the decimal digits 3, 6 and 911.5 %
A343810Numbers that contain only the digits 0,4,810.8 %
A365471Numbers whose digits are not all primes9.6 %