cp's OEIS Frontend

A296099 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, SumXOR_{k=1..n} a(k) is divisible by n, where SumXOR is the analog of summation under the binary XOR operation.

%I A296099 #20 Dec 09 2017 15:00:20
%S A296099 1,3,2,4,11,9,6,8,19,5,21,7,12,14,16,30,17,39,15,45,20,22,56,46,25,87,
%T A296099 31,33,74,36,32,62,66,96,34,72,109,37,78,54,42,44,40,86,90,116,112,94,
%U A296099 49,85,100,52,171,61,126,60,75,67,89,65,71,13,70,124,128
%N A296099 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, SumXOR_{k=1..n} a(k) is divisible by n, where SumXOR is the analog of summation under the binary XOR operation.
%C A296099 The partial XOR sums are given by A295907.
%C A296099 This sequence is a "binary" variant of A019444.
%C A296099 This sequence has connections with A286681; graphically, both sequences have similar fractal features; in the scatterplot of the current sequence, the rays emerging from the origin correspond to the numerous terms a(n) that are multiples of n.
%H A296099 Rémy Sigrist, <a href="/A296099/b296099.txt">Table of n, a(n) for n = 1..10000</a>
%H A296099 Rémy Sigrist, <a href="/A296099/a296099.png">Scatterplot of the first 2500000 terms</a>
%o A296099 (PARI) s = 0; x = 0; for (n=1, 65, for (k=1, oo, if (!bittest(s,k) && (xx=bitxor(x,k))%n==0, x = xx; s += 2^k; print1 (k ", "); break)))
%Y A296099 Cf. A019444, A286681, A295907.
%K A296099 nonn,look,base
%O A296099 1,2
%A A296099 _Rémy Sigrist_, Dec 04 2017