A219640 Numbers m for which there exists k such that m = 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

Author

Antti Karttunen, Nov 24 2012

Keywords

• nonn

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

Crossrefs

Cf. A007895, A022342, 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.

Programs

Scheme

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

Formula

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

Other identities. For all n >= 0:

A261093(a(n)) = n.

A261094(a(n)) = n.

Extensions

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