cp's OEIS Frontend

A297706 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).

%I A297706 #11 Jan 07 2018 23:49:06
%S A297706 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 A297706 29,38,36,31,40,32,23,42,34,25,44,48,27,41,33,35,39,43,37,51,45,49,53,
%U A297706 47,63,57,59,55,67,61,69,77,65,75,73,81,87,79,91,71,83
%N A297706 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 A297706 See A297879 for the corresponding prime numbers.
%C A297706 This sequence has connections with A076990: here we combine triples of successive terms with the XOR operator, there with the usual addition operator.
%C A297706 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 A297706 Rémy Sigrist, <a href="/A297706/b297706.txt">Table of n, a(n) for n = 1..10000</a>
%H A297706 Rémy Sigrist, <a href="/A297706/a297706.gp.txt">PARI program for A297706</a>
%H A297706 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 A297706 The first terms of the sequence are:
%e A297706     n     a(n)      a(n) XOR a(n+1) XOR a(n+2)
%e A297706   --    ----      --------------------------
%e A297706    1       1       7
%e A297706    2       2       5
%e A297706    3       4       2
%e A297706    4       3      13
%e A297706    5       5       7
%e A297706    6      11       5
%e A297706    7       9       2
%e A297706    8       7      13
%e A297706    9      12       2
%e A297706   10       6       3
%e A297706   11       8      11
%e A297706   12      13      19
%e A297706   13      14      17
%e A297706   14      16      13
%e A297706   15      15      23
%e A297706   16      18      11
%e A297706   17      10      13
%e A297706   18      19      17
%e A297706   19      20      19
%e A297706   20      22      31
%o A297706 (PARI) See Links section.
%Y A297706 Cf. A076990, A297879.
%K A297706 nonn,base
%O A297706 1,2
%A A297706 _Rémy Sigrist_, Jan 03 2018