Self-referential · 35 sequences
The sequences of the family “self-referential”, by A-number, with the share of their decomposable terms in the level class (k > L).
- primes · 1717
- polynomial · 1232
- quadratic form · 430
- prime values · 423
- residue class · 357
- digit rule · 306
- multiplicative · 199
- Beatty · 86
- divisor functions · 58
- binary rule · 48
- self-referential · 35
- complement · 23
- powers · 22
- summatory · 21
- arithmetic progression · 10
- smooth · 10
- forced divisor · 9
- sieve · 8
- block · 5
- base case · 1
| A-number | Name | Level |
|---|---|---|
| A001463 | Partial sums of A001462; also a(n) is the last occurrence of n in A001462 | 55.9 % |
| A002858 | Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms | 21.9 % |
| A002859 | a(1) = 1, a(2) = 3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n | 20.6 % |
| A002977 | Klarner-Rado sequence: a(1) = 1; subsequent terms are defined by the rule that if m is present so are 2m+1 and 3m+1 | 23.6 % |
| A002984 | a(0) = 1; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))) | 100.0 % |
| A005228 | Sequence and first differences (A030124) together list all positive numbers exactly once | 100.0 % |
| A005236 | Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n | 33.1 % |
| A005244 | A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence | 22.2 % |
| A005658 | If n appears so do 2n, 3n+2, 6n+3 | 13.5 % |
| A007378 | a(n), for n >= 2, is smallest positive integer which is consistent with sequence being monotonically increasing and satisfying a(a(n)) = 2n | 9.5 % |
| A023173 | Numbers k such that Fibonacci(k) == 1 (mod k) | 19.6 % |
| A030124 | Complement (and also first differences) of Hofstadter's sequence A005228 | 9.6 % |
| A036441 | a(n+1) = next number having largest prime dividing a(n) as a factor, with a(1) = 2 | 100.0 % |
| A045776 | a(n+1) is smallest multiple of (sum of digits of a(n)) which is > a(n) | 10.8 % |
| A045844 | a(n+1) = a(n) + largest digit of a(n); a(0) = 1 | 16.9 % |
| A052499 | If n is in the sequence then so are 2n and 4n-1 | 11.6 % |
| A057165 | Indices of addition steps in Recamán's sequence A005132 | 13.5 % |
| A061681 | a(0)=1; a(n) = a(n-1) + lead(a(n-1)) for n > 0 where for an integer x lead(x) is the leading digit in base 10 | 10.4 % |
| A064194 | a(2n) = 3*a(n), a(2n+1) = 2*a(n+1)+a(n), with a(1) = 1 | 56.7 % |
| A064437 | a(1)=1, a(n) = a(n-1) + 3 if n is already in the sequence, a(n) = a(n-1) + 2 otherwise | 15.0 % |
| A073121 | a(n) = r*a(ceiling(n/2)) + s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,2) | 100.0 % |
| A077477 | Least positive integers not excluded by the rule that if n is present then 2n+1 and 3n+1 are not allowed | 14.4 % |
| A078649 | Numbers n such that A000002(n)=A000002(n+1) where A000002 is the Kolakoski sequence | 16.2 % |
| A094222 | a(n+1) = a(n) + (number of distinct prime factors of a(n)) for n>1; a(1)=1, a(2)=2 | 12.3 % |
| A094589 | a(1) = 1; a(n+1) = a(n) + (largest element of {a} <= n) | 100.0 % |
| A096777 | a(n) = a(n-1) + Sum_{k=1..n-1}(a(k) mod 2), a(1) = 1 | 100.0 % |
| A147562 | Number of "ON" cells at n-th stage in the "Ulam-Warburton" two-dimensional cellular automaton | 70.9 % |
| A147991 | Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x+1 are in S | 9.3 % |
| A190803 | Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x-1 and 3x-1 are in a | 26.3 % |
| A191113 | Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 4x-2 are in a | 21.9 % |
| A250036 | Numbers n such that m = floor(n/4) is coprime to n and, if nonzero, m is also a term of the sequence | 11.8 % |
| A250046 | Numbers n such that m = floor(n/7) is coprime to n and, if nonzero, m is also a term of the sequence | 9.2 % |
| A250047 | Numbers n such that m = floor(n/7) is not coprime to n and, if nonzero, m is also a term of the sequence | 11.2 % |
| A250048 | Numbers n such that m = floor(n/6) is coprime to n and, if nonzero, m is also a term of the sequence | 8.6 % |
| A250049 | Numbers n such that m = floor(n/6) is not coprime to n and, if nonzero, m is also a term of the sequence | 14.8 % |