A337436 6*a(n) + 1 is the least upper prime p of a pair of twin primes p - 2, p, for which the prime gap immediately following p achieves the size 2*A007494(n).

1, 5, 23, 33, 322, 87, 325, 278, 495, 1293, 2027, 4725, 3468, 2690, 27177, 14438, 4245, 6773, 13283, 24938, 104283, 92067, 28893, 60015, 119362, 46905, 44270, 106323, 90713, 67475, 266618, 207107, 139708, 1496910, 716182, 598867, 439633, 688518, 224922, 315893

Offset

1,2

Comments

Apart from the atypical case [3, 5, 7], prime gaps nextprime(p+1)-p following a pair of twin primes p-2, p can only have the sizes 4, 6, 10, 12, 16, 18, ..., i.e., numbers k of the form 2*(k == 0 or 2 mod 3) = 2*A007494(n).

Links

Table of n, a(n) for n=1..40.

Example

a(1) = 1: The first occurrence of 3 consecutive primes [p-2, p, p+4] is at p = 6*a(1) + 1 = 7 -> [5, 7, 11],
a(2) = 5: consecutive primes [p-2, p, p+6] first occur at p = 6*a(2) * 1 = 31 -> [29, 31, 37],
a(3) = 23: consecutive primes [p-2, p, p+10] first occur at p = 6*a(3) + 1 = 139 -> [137, 139, 149].

Crossrefs

Cf. A007497, A329160, A329161, A337435.

Sequence in context: A238195 A231002 A329160 * A050906 A195974 A098421

Adjacent sequences: A337433 A337434 A337435 * A337437 A337438 A337439

Keyword

nonn

Author

Hugo Pfoertner, Sep 02 2020

Status

approved