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

Author

Antti Karttunen, Aug 09 2013

Keywords

• nonn

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.

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for Colombian or self numbers and related sequences

Crossrefs

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

Cf. A228085, A228086, A092391.