A228091 Numbers n for which there exists such a natural number k < n that k + bitcount(k) = n + bitcount(n), where bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

4, 12, 16, 17, 20, 28, 32, 34, 36, 44, 48, 49, 52, 60, 65, 68, 76, 80, 81, 84, 92, 96, 98, 100, 108, 112, 113, 116, 124, 128, 129, 130, 131, 132, 140, 144, 145, 148, 156, 160, 162, 164, 172, 176, 177, 180, 188, 193, 196, 204, 208, 209, 212, 220, 224, 226, 228

Offset

1,1

Comments

In other words, all such terms A228236(n) which satisfy A228236(n) > A228086(A092391(A228236(n))), which means that the sequence contains all natural numbers n such that A228085(A092391(n)) > 1 and n > A228086(A092391(n)).

Note: 124 is the first term that occurs both here and in A228237.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for Colombian or self numbers and related sequences

Example

For cases 0 + A000120(0) = 0, 1 + A000120(1) = 2, 2 + A000120(2) = 3, 3 + A000120(3) = 5 there are no smaller solutions yielding the same result.
However, for 4 + A000120(4) = 5, we already saw the case 3+A000120(3) giving the same result, thus 4 is the first term of this sequence.
Next time this occurs for 12, as 12 + A000120(12) = 14 = 11 + A000120(11), and 11 < 12.

Prog

(Scheme) ;; With Antti Karttunen's IntSeq-library.
(define A228091 (MATCHING-POS 1 1 (lambda (n) (> n (A228086 (A092391 n))))))

Crossrefs

Subset of A228236. Cf. also A228237. Complement of this sequence gives the nonzero terms of A228086 in ascending order.

Cf. A228085, A228086, A092391.

Sequence in context: A195547 A335528 A163838 * A157849 A137257 A368715

Adjacent sequences: A228088 A228089 A228090 * A228092 A228093 A228094

Keyword

nonn

Author

Antti Karttunen, Aug 09 2013

Status

approved