A228088 Numbers n for which there is a unique k which satisfies n = k + wt(k), where wt(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

0, 2, 3, 7, 8, 9, 10, 11, 12, 16, 20, 24, 25, 26, 27, 28, 29, 34, 35, 40, 41, 42, 43, 44, 45, 49, 53, 57, 58, 59, 60, 61, 62, 65, 66, 68, 69, 72, 73, 74, 75, 76, 77, 81, 85, 89, 90, 91, 92, 93, 94, 99, 100, 105, 106, 107, 108, 109, 110, 114, 118, 122, 123, 124

Offset

1,2

Comments

wt(k) = A000120(k) is also called bitcount(k).

In other words, the positions of ones in A228085.

Numbers that can be expressed as the sum of distinct terms of the form 2^n+1, n=0,1,... in exactly one way. - Matthew C. Russell, Oct 08 2013

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) = A092391(A228089(n)). [Consequence of the definitions of A228088 & A228089. Use the given Scheme-code to actually compute the sequence]

Example

0 is in this sequence because there is a unique k such that k+A000120(k)=0, in this case k=0.
1 is not in this sequence because there is no such k that k+A000120(k) would be 1. (Instead 1 is in A010061).
2 is in this sequence because there is exactly one k that satisfies k+A000120(k)=2, namely k=1.
3 is in this sequence because there is exactly one k that satisfies k+A000120(k)=3, namely k=2.
4 is not in this sequence because there is no such k that k+A000120(k) would be 4. (Instead 4 is in A010061.)
5 is not in this sequence because there is more than one k that satisfies k+A000120(k)=5, namely k=3 and k=4.

Maple

For Maple code see A230091. - N. J. A. Sloane, Oct 10 2013

Prog

(Scheme with Antti Karttunen's IntSeq-library)
(define A228088 (MATCHING-POS 1 0 (lambda (k) (= 1 (A228085 k)))))
(Haskell)
a228088 n = a228088_list !! (n-1)
a228088_list = 0 : filter ((== 1) . a228085) [1..]
-- Reinhard Zumkeller, Oct 13 2013

Crossrefs

Subset of A228082.

Cf. A228089 (corresponding k's for each a(n)).

Cf. A228090 (the same k's sorted into ascending order).

Cf. A000120, A228085, A092391, A010061, A010062, A230091, A230092, A230058.

Cf. A227915.

Sequence in context: A244162 A182516 A089008 * A299497 A047534 A353651

Adjacent sequences: A228085 A228086 A228087 * A228089 A228090 A228091

Keyword

nonn,base

Author

Antti Karttunen, Aug 09 2013

Status

approved