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

Author

Antti Karttunen, Aug 09 2013

Keywords

• nonn
• base

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

Examples

			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.
		

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 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.

Programs

Haskell

a228088 n = a228088_list !! (n-1)
a228088_list = 0 : filter ((== 1) . a228085) [1..]
-- Reinhard Zumkeller, Oct 13 2013

Maple

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

Formula

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