%I #12 Sep 03 2022 08:47:55

%S 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 67,31,29,37,39,45,41,43,47,53,55,61,63,59,70,42,71,50,74,51,75,54,

%U 130,46,82,131,58,134,83,49,81,57,85,133,69,135,77,73,79,87,91

%N 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 See A352723 for the corresponding prime numbers.

%C 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 Rémy Sigrist, <a href="/A352722/b352722.txt">Table of n, a(n) for n = 1..10000</a>

%e The first terms, alongside the corresponding prime numbers, are:

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

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

%e 1 2 2

%e 2 3 2

%e 3 6 2

%e 4 10 2

%e 5 7 5

%e 6 5 5

%e 7 13 13

%e 8 15 11

%e 9 11 2

%e 10 18 2

%o (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 Cf. A102211, A308334 (OR variant), A336817 (XOR variant), A352723.

%K nonn,base

%O 1,1

%A _Rémy Sigrist_, Mar 30 2022