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A296615 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n) XOR a(n+1) is a cube (where XOR denotes the XOR binary operator). 2

%I

%S 1,9,8,19,18,26,27,91,38,39,47,46,53,52,60,61,64,65,73,72,83,82,90,

%T 130,131,139,138,145,144,152,153,217,164,124,103,102,110,111,116,117,

%U 125,165,173,172,183,182,190,191,194,195,203,202,209,208,216,399,343

%N Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, a(n) XOR a(n+1) is a cube (where XOR denotes the XOR binary operator).

%C This sequence has similarities with A175428: here a(n) XOR a(n+1) is a cube, there a(n) + a(n+1) is a cube.

%C This sequence is conjectured to the a permutation of the natural numbers.

%C The first fixed points are: 1, 5676, 5677, 5698, 11677, 13226, 26943, 26946, 27575, 28039, 28569, 28625, 30127, 30162, 37660, 37661, 44672, 44673, 45934.

%C The scatterplot of the first terms of the sequence shows hatches (see Links section).

%H Rémy Sigrist, <a href="/A296615/b296615.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A296615/a296615.png">Scatterplot of the first 50000 terms</a>

%e The first terms, alongside a(n) XOR a(n+1), are:

%e n a(n) a(n) XOR a(n+1)

%e -- ---- ---------------

%e 1 1 2^3

%e 2 9 1^3

%e 3 8 3^3

%e 4 19 1^3

%e 5 18 2^3

%e 6 26 1^3

%e 7 27 4^3

%e 8 91 5^3

%e 9 38 1^3

%e 10 39 2^3

%e 11 47 1^3

%e 12 46 3^3

%e 13 53 1^3

%e 14 52 2^3

%e 15 60 1^3

%e 16 61 5^3

%e 17 64 1^3

%e 18 65 2^3

%e 19 73 1^3

%e 20 72 3^3

%o (PARI) seen = 0; unseen = 1

%o other(p) = seen += 2^p; while (bittest(seen, unseen), unseen++); \

%o for (v=unseen, oo, if (!bittest(seen, v) && ispower(bitxor(p,v),3), return (v)))

%o for (n=1, 57, v=if (n==1, 1, other(v)); print1 (v ", "))

%Y Cf. A000578, A175428.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Dec 17 2017

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Last modified June 19 05:18 EDT 2021. Contains 345125 sequences. (Running on oeis4.)