A228089 Integers k for which a sum k + bitcount(k) cannot be obtained as a sum k2 + bitcount(k2) for any other k2<>k.

0, 1, 2, 5, 6, 8, 7, 9, 10, 13, 18, 21, 22, 24, 23, 25, 26, 30, 33, 37, 38, 40, 39, 41, 42, 45, 50, 53, 54, 56, 55, 57, 58, 64, 61, 66, 63, 69, 70, 72, 71, 73, 74, 77, 82, 85, 86, 88, 87, 89, 90, 94, 97, 101, 102, 104, 103, 105, 106, 109, 114, 117, 118, 120, 119

Offset

1,3

Comments

The values of k's are sorted here according to the magnitude of the sum k + bitcount(k), where bitcount(k) (= A000120) gives the number of 1's in binary representation of nonnegative integer k; a(n) = A228086(A228088(n)).

Links

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

Index entries for Colombian or self numbers and related sequences

Formula

a(n) = A228086(A228088(n)).

A092391(a(n)) = A228088(n).

Example

6 is in this sequence because the sum 6+A000120(6)=8 cannot be obtained with any other value of k than k=6.
8 is in this sequence because the sum 8+A000120(8)=9 cannot be obtained with any other value of k than k=8.
7 is in this sequence because the sum 7+A000120(7)=10 cannot be obtained with any other value of k than k=7.
In this sequence 8 becomes before 7 because 8+A000120(8) < 7+A000120(7).

Prog

(Scheme) (define (A228089 n) (A228086 (A228088 n)))

Crossrefs

A228090 gives the same terms sorted into ascending order.

Sequence in context: A167455 A159752 A352325 * A126971 A175354 A224778

Adjacent sequences: A228086 A228087 A228088 * A228090 A228091 A228092

Keyword

nonn

Author

Antti Karttunen, Aug 17 2013

Status

approved