cp's OEIS Frontend

A286709 For k>0, let bin(k) = the string corresponding to the binary representation of k, and neg(k) = bin(k) under the character substitution '0' <-> '1'; a(n) = the smallest positive integer not occurring earlier in the sequence such that bin(Sum_{k=1..n} a(k)) contains neg(n) as a substring.

%I A286709 #7 May 13 2017 23:47:13
%S A286709 2,3,4,10,1,5,7,14,8,15,11,19,31,6,24,28,18,12,50,32,30,9,21,38,13,42,
%T A286709 63,20,16,25,64,61,51,44,27,35,89,37,87,39,85,41,83,17,107,45,79,29,
%U A286709 52,92,75,22,102,53,71,40,43,34,23,103,127,128,62,188,66,60
%N A286709 For k>0, let bin(k) = the string corresponding to the binary representation of k, and neg(k) = bin(k) under the character substitution '0' <-> '1'; a(n) = the smallest positive integer not occurring earlier in the sequence such that bin(Sum_{k=1..n} a(k)) contains neg(n) as a substring.
%C A286709 When considering bin(k), all leading zeros are removed: bin(2) = "10".
%C A286709 When considering neg(k), all leading zeros are preserved: neg(2) = "01".
%C A286709 The scatterplots of this sequence and of A160855 show similar entanglements of lines.
%C A286709 Partial sums are given by A286713.
%H A286709 Rémy Sigrist, <a href="/A286709/b286709.txt">Table of n, a(n) for n = 1..10000</a>
%H A286709 Rémy Sigrist, <a href="/A286709/a286709.pl.txt">Perl program for A286709</a>
%H A286709 Rémy Sigrist, <a href="/A286709/a286709.pdf">Illustration of first terms</a>
%Y A286709 Cf. A160855, A286713.
%K A286709 nonn,base,look
%O A286709 1,1
%A A286709 _Rémy Sigrist_, May 13 2017