cp's OEIS Frontend

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.

%I A219640 #26 Jul 17 2025 14:51:20
%S A219640 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,
%T A219640 38,40,41,42,45,46,47,49,50,54,55,56,58,59,61,62,63,66,67,68,70,71,74,
%U A219640 75,76,78,79,81,82,83,88,89,90,92,93,95,96,97,100,101,102
%N 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.
%C A219640 These are the positive integers i for which there exists k such that A007895(i+k)=k.
%C A219640 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.
%H A219640 Antti Karttunen, <a href="/A219640/b219640.txt">Table of n, a(n) for n = 0..10947</a>
%F A219640 a(n) = A219641(A022342(n+1)).
%F A219640 Other identities. For all n >= 0:
%F A219640 A261093(a(n)) = n.
%F A219640 A261094(a(n)) = n.
%o A219640 (Scheme) (define (A219640 n) (A219641 (A022342 (+ 1 n))))
%Y A219640 Cf. A007895, A022342, A219641. Complement: A219638. Union of A219639 and A219637.
%Y A219640 First differences: A261095.
%Y A219640 Characteristic function: A261092.
%Y A219640 Left inverses: A261093, A261094.
%Y A219640 Analogous sequences for other bases: A005187, A219650.
%K A219640 nonn
%O A219640 0,3
%A A219640 _Antti Karttunen_, Nov 24 2012
%E A219640 Starting offset changed to 0 by _Antti Karttunen_, Aug 08 2015