A286681 - OEIS

A286681

a(n) = the smallest positive integer not occurring earlier in the sequence such that SumXOR_{k=1..n} a(k) written in binary contains binary n as a substring, where SumXOR is the analog of summation under the binary XOR operation.

%I #19 May 13 2017 23:47:03

%S 1,3,4,2,9,11,8,6,17,12,14,7,33,5,23,15,49,35,20,18,30,28,24,22,10,40,

%T 44,42,38,36,32,94,34,96,65,43,45,41,107,79,58,56,60,122,118,52,48,46,

%U 19,81,84,82,95,29,25,31,73,67,13,75,70,68,64,62,129,69

%N a(n) = the smallest positive integer not occurring earlier in the sequence such that SumXOR_{k=1..n} a(k) written in binary contains binary n as a substring, where SumXOR is the analog of summation under the binary XOR operation.

%C This sequence is a variant of A160855: here we consider SumXOR, there Sum.

%C The partial XOR sums are given by A286712.

%H Rémy Sigrist, <a href="/A286681/b286681.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A286681/a286681.pl.txt">Perl program for A286681</a>

%H Rémy Sigrist, <a href="/A286681/a286681.pdf">Illustration of the first terms</a>

%Y Cf. A160855, A286712.

%K nonn,base,look

%O 1,2

%A _Rémy Sigrist_, May 13 2017