A337435 6*a(n) - 1 is the least prime p of a pair of twin primes p, p + 2, for which the prime gap immediately below p achieves the size 2*A007494(n).

2, 5, 25, 87, 325, 213, 192, 758, 500, 1158, 1668, 5383, 4217, 13130, 15180, 4713, 5955, 19583, 66642, 17127, 48108, 49485, 28905, 171005, 175530, 61838, 314192, 76967, 192637, 96147, 812768, 708780, 139725, 295862, 354545, 1572328, 1240860, 1681368, 773453, 1300602

Offset

1,1

Comments

Apart from the atypical case [3, 5, 7], prime gaps p - prevprime(p-1) preceding a pair of twin primes p, p+2 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) = 2: The first occurrence of 3 consecutive primes [p-4, p, p+2] is at p = 6*a(1) - 1 = 11 -> [7, 11, 13],
a(2) = 5: consecutive primes [p-6, p, p+2] first occur at p = 6*a(2) - 1 = 29 -> [23, 29, 31],
a(3) = 25: consecutive primes [p-10, p, p+2] first occur at p = 6*a(3) - 1 = 149 -> [139, 149, 151].

Crossrefs

Cf. A007494, A329158, A329159, A337436.

Sequence in context: A349146 A268356 A329158 * A074417 A296105 A268120

Adjacent sequences: A337432 A337433 A337434 * A337436 A337437 A337438

Keyword

nonn

Author

Hugo Pfoertner, Sep 02 2020

Status

approved