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A352722 Lexicographically earliest sequence of distinct positive integers such that a(1) = 2 and for any n > 0, a(n) AND a(n+1) is prime (where AND denotes the bitwise AND operator).

%I A352722 #12 Sep 03 2022 08:47:55
%S A352722 2,3,6,10,7,5,13,15,11,18,14,19,17,21,25,23,27,34,22,35,26,38,66,30,
%T A352722 67,31,29,37,39,45,41,43,47,53,55,61,63,59,70,42,71,50,74,51,75,54,
%U A352722 130,46,82,131,58,134,83,49,81,57,85,133,69,135,77,73,79,87,91
%N A352722 Lexicographically earliest sequence of distinct positive integers such that a(1) = 2 and for any n > 0, a(n) AND a(n+1) is prime (where AND denotes the bitwise AND operator).
%C A352722 See A352723 for the corresponding prime numbers.
%C A352722 Terms of A102211 clearly do not occur in this sequence. Is this a permutation of the complement of A102211 in the positive integers? - _Peter Munn_, Sep 02 2022
%H A352722 Rémy Sigrist, <a href="/A352722/b352722.txt">Table of n, a(n) for n = 1..10000</a>
%e A352722 The first terms, alongside the corresponding prime numbers, are:
%e A352722   n   a(n)  a(n) AND a(n+1)
%e A352722   --  ----  ---------------
%e A352722    1     2                2
%e A352722    2     3                2
%e A352722    3     6                2
%e A352722    4    10                2
%e A352722    5     7                5
%e A352722    6     5                5
%e A352722    7    13               13
%e A352722    8    15               11
%e A352722    9    11                2
%e A352722   10    18                2
%o A352722 (PARI) s=0; v=2; for (n=1, 65, print1 (v", "); s+=2^v; for (w=1, oo, if (!bittest(s, w) && isprime(bitand(v,w)), v=w; break)))
%Y A352722 Cf. A102211, A308334 (OR variant), A336817 (XOR variant), A352723.
%K A352722 nonn,base
%O A352722 1,1
%A A352722 _Rémy Sigrist_, Mar 30 2022