A230297 a(n) = A010062(n) written in binary: a(n+1) = a(n) + hammingweight(a(n)) in binary.

1, 10, 11, 101, 111, 1010, 1100, 1110, 10001, 10011, 10110, 11001, 11100, 11111, 100100, 100110, 101001, 101100, 101111, 110100, 110111, 111100, 1000000, 1000001, 1000011, 1000110, 1001001, 1001100, 1001111, 1010100, 1010111, 1011100, 1100000, 1100010, 1100101, 1101001, 1101101, 1110010, 1110110, 1111011, 10000001, 10000011

Offset: 0

Author

N. J. A. Sloane, Oct 17 2013

Keywords

• nonn
• base

Comments

Is there any way to tell by looking at a binary number whether or not it is a term of this sequence?

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000
• Index entries for Colombian or self numbers and related sequences.

Crossrefs

Cf. A010062.

Essentially the same as A157845.

Cf. A004207 (base-10 analog); A007088 (n in binary), A010062 (this written in base 10), A000120 (Hammingweight), A092391 (A000120(n) + n), A028897 (convert binary to decimal).

Programs

Mathematica

s[0] = 1; s[n_] := s[n] = s[n-1] + DigitCount[s[n-1], 2, 1]; Table[FromDigits[IntegerDigits[s[n], 2]], {n, 0, 50}] (* Amiram Eldar, Jul 28 2023 *)

PARI

(A230297(n)=A007088(A010062(n))); A230297_vec(N)={vector(N,i, if(i>1, A007088(N+=hammingweight(N)), N=1))} \\ M. F. Hasler, Nov 18 2019

Formula

a(n) = A157845(n+1) = A007088(A010062(n)) = A007088(A092391(A028897(a(n-1)))). - M. F. Hasler, Nov 18 2019