A336817 -id:A336817 - cp's OEIS frontend

A337013 Prime numbers arising in A336817.

3, 7, 3, 5, 7, 3, 13, 2, 3, 2, 5, 2, 3, 2, 31, 2, 3, 2, 7, 2, 3, 2, 13, 2, 3, 2, 5, 2, 3, 2, 61, 2, 3, 2, 5, 2, 3, 2, 13, 2, 3, 2, 5, 2, 3, 2, 31, 2, 3, 2, 7, 2, 3, 2, 13, 2, 3, 2, 5, 2, 3, 2, 127, 2, 3, 2, 7, 2, 3, 2, 13, 2, 3, 2, 5, 2, 3, 2, 31, 2, 3, 2, 7

Offset: 1

Rémy Sigrist, Nov 21 2020

This sequence contains large runs of consecutive terms that are repeated later on.

			a(7) = A336817(7) XOR A336817(8) = 7 XOR 10 = 13.

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

Cf. A308340, A336817.

s=0; v=1; for (n=1, 83, s+=2^v; for (w=1, oo, if (!bittest(s, w) && isprime(p=bitxor(v, w)), print1 (p ", "); v=w; break)))

a(n) = A336817(n) XOR A336817(n+1) (where XOR denotes the bitwise XOR operator).

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).

Original entry on oeis.org

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

Rémy Sigrist, Mar 30 2022

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

			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

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

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

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)))

cp's OEIS Frontend

A337013 Prime numbers arising in A336817.

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