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).

2, 3, 6, 10, 7, 5, 13, 15, 11, 18, 14, 19, 17, 21, 25, 23, 27, 34, 22, 35, 26, 38, 66, 30, 67, 31, 29, 37, 39, 45, 41, 43, 47, 53, 55, 61, 63, 59, 70, 42, 71, 50, 74, 51, 75, 54, 130, 46, 82, 131, 58, 134, 83, 49, 81, 57, 85, 133, 69, 135, 77, 73, 79, 87, 91

Offset: 1

Author

Rémy Sigrist, Mar 30 2022

Keywords

• nonn
• base

Comments

See A352723 for the corresponding prime numbers.

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

Examples

			The first terms, alongside the corresponding prime numbers, are:
  n   a(n)  a(n) AND a(n+1)
  --  ----  ---------------
   1     2                2
   2     3                2
   3     6                2
   4    10                2
   5     7                5
   6     5                5
   7    13               13
   8    15               11
   9    11                2
  10    18                2
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

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)))