A228086 a(n) is the least k which satisfies n = k + bitcount(k), or 0 if no such k exists. Here bitcount(k) (or wt(k), A000120) gives the number of 1's in binary representation of nonnegative integer k.

0, 0, 1, 2, 0, 3, 0, 5, 6, 8, 7, 9, 10, 0, 11, 0, 13, 14, 0, 15, 18, 0, 19, 0, 21, 22, 24, 23, 25, 26, 0, 27, 0, 29, 30, 33, 31, 0, 35, 0, 37, 38, 40, 39, 41, 42, 0, 43, 0, 45, 46, 0, 47, 50, 0, 51, 0, 53, 54, 56, 55, 57, 58, 0, 59, 64, 61, 62, 66, 63, 67, 0

Offset

0,4

Comments

A083058(n)+1 gives a lower bound for nonzero terms, n-1 an upper bound.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for Colombian or self numbers and related sequences

Mathematica

a[n_] := Module[{k}, For[k = n - Floor[Log[2, n]] - 1, k < n, k++, If[n == k + DigitCount[k, 2, 1], Return[k]]]; 0];
a /@ Range[0, 1000]; (* Jean-François Alcover, Nov 28 2020 *)

Prog

(Scheme) (define (A228086 n) (if (zero? n) n (let loop ((k (+ (A083058 n) 1))) (cond ((> k n) 0) ((= n (A092391 k)) k) (else (loop (+ 1 k)))))))

Crossrefs

Cf. A228087, A228085, A335599. A010061 gives the positions of zeros after a(0). The union of A010061 and A228088 gives the positions where a(n) = A228087(n).

Cf. also A213723, A227643.

Sequence in context: A138325 A258323 A117175 * A090482 A082857 A208092

Adjacent sequences: A228083 A228084 A228085 * A228087 A228088 A228089

Keyword

nonn

Author

Antti Karttunen, Aug 09 2013

Status

approved