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