Binary rule · 48 sequences
The sequences of the family “binary rule”, 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 |
|---|---|---|
| A000069 | Odious numbers: numbers with an odd number of 1's in their binary expansion | 11.0 % |
| A000695 | Moser-de Bruijn sequence: sums of distinct powers of 4 | 14.0 % |
| A001196 | Double-bitters: only even length runs in binary expansion | 14.0 % |
| A001969 | Evil numbers: nonnegative integers with an even number of 1's in their binary expansion | 11.4 % |
| A003159 | Numbers whose binary representation ends in an even number of zeros | 13.9 % |
| A003607 | Location of 0's when natural numbers are listed in binary | 12.9 % |
| A003714 | Fibbinary numbers: if n = F(i1) + F(i2) + ... + F(ik) is the Zeckendorf representation of n (i.e., write n in Fibonacci number system) then a(n) = 2^(i1 - 2) + 2^(i2 - 2) + ... + 2^(ik - 2). Also numbers whose binary representation contains no two adjacent 1's | 10.4 % |
| A003726 | Numbers with no 3 adjacent 1's in binary expansion | 9.9 % |
| A003754 | Numbers with no adjacent 0's in binary expansion | 11.6 % |
| A003796 | Numbers with no 3 adjacent 0's in binary expansion | 10.6 % |
| A004742 | Numbers whose binary expansion does not contain 101 | 13.6 % |
| A004743 | Numbers whose binary expansion does not contain 110 | 11.4 % |
| A004744 | Numbers whose binary expansion does not contain 011 | 11.3 % |
| A004745 | Numbers whose binary expansion does not contain 001 | 10.1 % |
| A004746 | Numbers whose binary expansion does not contain 010 | 12.1 % |
| A004780 | Binary expansion contains 2 adjacent 1's | 9.7 % |
| A006364 | Numbers k with an even number of 1's in binary, ignoring last bit | 13.1 % |
| A006995 | Binary palindromes: numbers whose binary expansion is palindromic | 88.4 % |
| A007088 | The binary numbers (or binary words, or binary vectors, or binary expansion of n): numbers written in base 2 | 12.7 % |
| A010061 | Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of m | 17.1 % |
| A014312 | Numbers with exactly 4 ones in binary expansion | 12.9 % |
| A014313 | Numbers with exactly 5 ones in binary expansion | 8.9 % |
| A022155 | Values of n at which Golay-Rudin-Shapiro sequence A020985 is negative | 11.5 % |
| A023688 | Numbers with exactly 6 ones in binary expansion | 8.9 % |
| A023689 | Numbers with exactly 7 ones in binary expansion | 9.4 % |
| A023690 | Numbers with exactly 8 ones in binary expansion | 11.4 % |
| A023691 | Numbers with exactly 9 ones in binary expansion | 12.2 % |
| A026430 | a(n) is the sum of first n terms of A001285 (Thue-Morse sequence) | 17.5 % |
| A031443 | Digitally balanced numbers: positive numbers that in base 2 have the same number of 0's as 1's | 11.8 % |
| A033015 | Numbers whose base-2 expansion has no run of digits with length < 2 | 19.1 % |
| A035928 | Numbers n such that BCR(n) = n, where BCR = binary-complement-and-reverse = take one's complement then reverse bit order | 84.4 % |
| A036554 | Numbers whose binary representation ends in an odd number of zeros | 13.9 % |
| A036990 | Numbers n such that, in the binary expansion of n, reading from right to left, the number of 1's never exceeds the number of 0's | 4.7 % |
| A048701 | List of binary palindromes of even length (written in base 10) | 87.8 % |
| A049445 | Numbers k with the property that the number of 1's in binary expansion of k (see A000120) divides k | 19.0 % |
| A063037 | Numbers without 3 consecutive equal binary digits | 10.2 % |
| A077436 | Let B(n) be the sum of binary digits of n. This sequence contains n such that B(n) = B(n^2) | 28.5 % |
| A079523 | Utterly odd numbers: numbers whose binary representation ends in an odd number of ones | 20.6 % |
| A090050 | Numbers having equal length of longest contiguous block of zeros and ones in binary expansion | 14.0 % |
| A090421 | Numbers that can be written in binary representation as concatenation of primes | 14.3 % |
| A091067 | Numbers whose odd part is of the form 4*k+3 | 13.1 % |
| A091072 | Positive numbers k such that the Kronecker Symbol (-1 / k) > 0 | 13.1 % |
| A101082 | Numbers n such that binary representation contains bit strings "10" and "01" (possibly overlapping) | 9.6 % |
| A121539 | Numbers whose binary expansion ends in an even number of 1's | 12.0 % |
| A131323 | Odd numbers whose binary expansion ends in an even number of 1's | 25.6 % |
| A203463 | Where Golay-Rudin-Shapiro sequence A020985 is positive | 11.1 % |
| A230091 | Numbers of the form k + wt(k) for exactly two distinct k, where wt(k) = A000120(k) is the binary weight of k | 17.6 % |
| A230092 | Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of k | 30.4 % |