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).
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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Sep 02 2020
STATUS
approved