

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.


6



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
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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 IntSeqlibrary)
(define A228091 (MATCHINGPOS 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: A224785 A195547 A163838 * A157849 A137257 A144976
Adjacent sequences: A228088 A228089 A228090 * A228092 A228093 A228094


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 09 2013


STATUS

approved



