A219640 Numbers n for which there exists k such that n = k - (number of 1's in Zeckendorf expansion of k); distinct values in A219641.

0, 1, 2, 4, 5, 7, 8, 9, 12, 13, 14, 16, 17, 20, 21, 22, 24, 25, 27, 28, 29, 33, 34, 35, 37, 38, 40, 41, 42, 45, 46, 47, 49, 50, 54, 55, 56, 58, 59, 61, 62, 63, 66, 67, 68, 70, 71, 74, 75, 76, 78, 79, 81, 82, 83, 88, 89, 90, 92, 93, 95, 96, 97, 100, 101, 102

Offset

0,3

Comments

These are the positive integers i for which there exists k such that A007895(i+k)=k.

Starting offset is zero, because a(0) = 0 is a special case. Start indexing from 1 when you want only nonzero natural numbers satisfying the same condition.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10947

Formula

a(n) = A219641(A022342(n+1)).

Other identities. For all n >= 0:

A261093(a(n)) = n.

A261094(a(n)) = n.

Prog

(Scheme): (define (A219640 n) (A219641 (A022342 (+ 1 n))))

Crossrefs

Cf. A219641. Complement: A219638. Union of A219639 and A219637.

First differences: A261095.

Characteristic function: A261092.

Left inverses: A261093, A261094.

Analogous sequences for other bases: A005187, A219650.

Sequence in context: A345917 A303739 A183544 * A344406 A184164 A190852

Adjacent sequences: A219637 A219638 A219639 * A219641 A219642 A219643

Keyword

nonn

Author

Antti Karttunen, Nov 24 2012

Extensions

Starting offset changed to 0 by Antti Karttunen, Aug 08 2015

Status

approved