A228237 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.

3, 11, 14, 15, 19, 27, 29, 31, 35, 43, 46, 47, 51, 59, 62, 67, 75, 78, 79, 83, 91, 93, 95, 99, 107, 110, 111, 115, 123, 124, 125, 126, 127, 131, 139, 142, 143, 147, 155, 157, 159, 163, 171, 174, 175, 179, 187, 190, 195, 203, 206, 207, 211, 219, 221, 223, 227

Offset

1,1

Comments

In other words, all such terms A228236(n) which satisfy A228236(n) < A228087(A092391(A228236(n))).

Note: 124 is the first term that occurs both here and in A228091.

Links

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

Example

For cases 0 + A000120(0) = 0, 1 + A000120(1) = 2, 2 + A000120(2) = 3 there are no larger solutions yielding the same result.
However, for 3 + A000120(3) = 5 there is a larger solution yielding the same result, namely 4 + A000120(4) = 5, thus 3 is the first term of this sequence.
Next time this occurs for 11, as 11 + A000120(11) = 14 = 12 + A000120(12), and 12 > 11.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(define A228237 (MATCHING-POS 1 1 (lambda (n) (< n (A228087 (A092391 n))))))

Crossrefs

Subset of A228236. Cf. also A228091.

Sequence in context: A201426 A158790 A176049 * A186078 A224857 A322608

Adjacent sequences: A228234 A228235 A228236 * A228238 A228239 A228240

Keyword

nonn

Author

Antti Karttunen, Sep 11 2013

Status

approved