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

1,1

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

Links

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

Example

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

Prog

(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)))

Crossrefs

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

Sequence in context: A191668 A056060 A056058 * A028255 A342766 A048633

Adjacent sequences: A352719 A352720 A352721 * A352723 A352724 A352725

Keyword

nonn,base

Author

Rémy Sigrist, Mar 30 2022

Status

approved