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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. 2

%I #7 May 13 2017 23:47:13

%S 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 63,20,16,25,64,61,51,44,27,35,89,37,87,39,85,41,83,17,107,45,79,29,

%U 52,92,75,22,102,53,71,40,43,34,23,103,127,128,62,188,66,60

%N 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 When considering bin(k), all leading zeros are removed: bin(2) = "10".

%C When considering neg(k), all leading zeros are preserved: neg(2) = "01".

%C The scatterplots of this sequence and of A160855 show similar entanglements of lines.

%C Partial sums are given by A286713.

%H Rémy Sigrist, <a href="/A286709/b286709.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A286709/a286709.pl.txt">Perl program for A286709</a>

%H Rémy Sigrist, <a href="/A286709/a286709.pdf">Illustration of first terms</a>

%Y Cf. A160855, A286713.

%K nonn,base,look

%O 1,1

%A _Rémy Sigrist_, May 13 2017

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Last modified August 28 09:38 EDT 2024. Contains 375481 sequences. (Running on oeis4.)