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%I #11 Jan 07 2018 23:49:06
%S 1,2,4,3,5,11,9,7,12,6,8,13,14,16,15,18,10,19,20,22,17,24,26,21,28,30,
%T 29,38,36,31,40,32,23,42,34,25,44,48,27,41,33,35,39,43,37,51,45,49,53,
%U 47,63,57,59,55,67,61,69,77,65,75,73,81,87,79,91,71,83
%N Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) XOR a(n+1) XOR a(n+2) is prime (where XOR denotes the bitwise XOR operator).
%C See A297879 for the corresponding prime numbers.
%C This sequence has connections with A076990: here we combine triples of successive terms with the XOR operator, there with the usual addition operator.
%C The sequence alternates long runs of odd terms and long runs with periodic parity (even, even, odd); changes from one type of run to the other occur near terms such that a(n) XOR a(n+1) XOR a(n+2) = 2; see illustration in Links section.
%H Rémy Sigrist, <a href="/A297706/b297706.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A297706/a297706.gp.txt">PARI program for A297706</a>
%H Rémy Sigrist, <a href="/A297706/a297706.png">Colored scatterplot of the first 25000 terms</a> (where the color is function of the parity of a(n))
%e The first terms of the sequence are:
%e n a(n) a(n) XOR a(n+1) XOR a(n+2)
%e -- ---- --------------------------
%e 1 1 7
%e 2 2 5
%e 3 4 2
%e 4 3 13
%e 5 5 7
%e 6 11 5
%e 7 9 2
%e 8 7 13
%e 9 12 2
%e 10 6 3
%e 11 8 11
%e 12 13 19
%e 13 14 17
%e 14 16 13
%e 15 15 23
%e 16 18 11
%e 17 10 13
%e 18 19 17
%e 19 20 19
%e 20 22 31
%o (PARI) See Links section.
%Y Cf. A076990, A297879.
%K nonn,base
%O 1,2
%A _Rémy Sigrist_, Jan 03 2018