A388062 Least prime p such that p+A135311(k) is prime for 2 <= k <= n, but not for k = n+1, or 0 if no such prime exists.

2, 3, 17, 191, 101, 5, 165701, 15760091, 182403491, 33081664151, 7908189600581, 380284918609481, 7933248530182091, 21817283854511261, 44360646117391789301

Offset

1,1

Comments

If the first Hardy-Littlewood conjecture (or the k-tuple conjecture) holds, a(n) != 0 for all n.

a(24) = 11.

Links

Table of n, a(n) for n=1..15.

Wikipedia, First Hardy-Littlewood conjecture.

Wikipedia, Prime k-tuple.

Example

For n = 5, the smallest prime p such that p+2, p+6, p+8, and p+12 are prime, but p+18 is not prime, is a(5) = 101.
For 1 <= n <= 15 (except n = 6), a(n) is the first term p in the following sequences such that p+A135311(n+1) is not prime:
  a( 1) = A000040(1);
  a( 2) = A001359(1);
  a( 3) = A022004(3);
  a( 4) = A007530(4);
  a( 5) = A022006(3);
  a( 7) = A022009(2);
  a( 8) = A022011(2);
  a( 9) = A022545(2);
  a(10) = A027569(2);
  a(11) = A213647(2);
  a(12) = A213645(2);
  a(13) = A257139(2);
  a(14) = A257167(2);
  a(15) = A257304(2).

Crossrefs

Cf. A135311.

Cf. A000040, A001359, A022004, A007530, A022006, A022009, A022011, A022545, A027569, A213647, A213645, A257139, A257167, A257304.

Sequence in context: A328340 A042978 A089675 * A041383 A389935 A042903

Adjacent sequences: A388059 A388060 A388061 * A388063 A388064 A388065

Keyword

nonn,more

Author

Pontus von Brömssen, Sep 14 2025

Status

approved