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Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) XOR a(n+1) is a prime number as small as possible (where XOR denotes the bitwise XOR operator).
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%I #13 Jan 10 2021 22:19:34

%S 0,2,1,3,6,4,7,5,14,12,15,13,8,10,9,11,26,24,27,25,28,30,29,31,20,22,

%T 21,23,18,16,19,17,52,54,53,55,50,48,51,49,58,56,59,57,60,62,61,63,46,

%U 44,47,45,40,42,41,43,32,34,33,35,38,36,39,37,102,100,103

%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) XOR a(n+1) is a prime number as small as possible (where XOR denotes the bitwise XOR operator).

%C This sequence has connections with A003188; their scatterplots are alike.

%C This sequence appears to be a permutation of the nonnegative integers.

%H Rémy Sigrist, <a href="/A340406/b340406.txt">Table of n, a(n) for n = 0..8191</a>

%H Rémy Sigrist, <a href="/A340406/a340406.png">Scatterplot of the first 2^16 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 0 0 2

%e 1 2 3

%e 2 1 2

%e 3 3 5

%e 4 6 2

%e 5 4 3

%e 6 7 2

%e 7 5 11

%e 8 14 2

%e 9 12 3

%e 10 15 2

%e 11 13 5

%e 12 8 2

%o (PARI) s=0; v=0; for (n=0, 66, print1 (v", "); s+=2^v; forprime (p=2, oo, if (!bittest(s, w=bitxor(v,p)), v=w; break)))

%Y Cf. A003188, A340446 (cube analog), A340447 (Fibonacci analog).

%K nonn,base

%O 0,2

%A _Rémy Sigrist_, Jan 06 2021