cp's OEIS Frontend

A228086 a(n) is the least k which satisfies n = k + bitcount(k), or 0 if no such k exists. Here bitcount(k) (or wt(k), A000120) gives the number of 1's in binary representation of nonnegative integer k.

%I A228086 #23 Nov 28 2020 09:10:11
%S A228086 0,0,1,2,0,3,0,5,6,8,7,9,10,0,11,0,13,14,0,15,18,0,19,0,21,22,24,23,
%T A228086 25,26,0,27,0,29,30,33,31,0,35,0,37,38,40,39,41,42,0,43,0,45,46,0,47,
%U A228086 50,0,51,0,53,54,56,55,57,58,0,59,64,61,62,66,63,67,0
%N A228086 a(n) is the least k which satisfies n = k + bitcount(k), or 0 if no such k exists. Here bitcount(k) (or wt(k), A000120) gives the number of 1's in binary representation of nonnegative integer k.
%C A228086 A083058(n)+1 gives a lower bound for nonzero terms, n-1 an upper bound.
%H A228086 Antti Karttunen, <a href="/A228086/b228086.txt">Table of n, a(n) for n = 0..8192</a>
%H A228086 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%t A228086 a[n_] := Module[{k}, For[k = n - Floor[Log[2, n]] - 1, k < n, k++, If[n == k + DigitCount[k, 2, 1], Return[k]]]; 0];
%t A228086 a /@ Range[0, 1000]; (* _Jean-François Alcover_, Nov 28 2020 *)
%o A228086 (Scheme) (define (A228086 n) (if (zero? n) n (let loop ((k (+ (A083058 n) 1))) (cond ((> k n) 0) ((= n (A092391 k)) k) (else (loop (+ 1 k)))))))
%Y A228086 Cf. A228087, A228085, A335599. A010061 gives the positions of zeros after a(0). The union of A010061 and A228088 gives the positions where a(n) = A228087(n).
%Y A228086 Cf. also A213723, A227643.
%K A228086 nonn
%O A228086 0,4
%A A228086 _Antti Karttunen_, Aug 09 2013