A182481 a(n) is the least k such that 6*k*n-1 and 6*k*n+1 are twin primes, and a(n)=0, if such k does not exist.

1, 1, 1, 3, 1, 2, 1, 4, 2, 1, 3, 1, 4, 5, 2, 2, 1, 1, 2, 2, 7, 5, 1, 3, 1, 2, 5, 16, 2, 1, 7, 1, 1, 5, 2, 2, 9, 1, 8, 1, 5, 9, 4, 5, 1, 3, 1, 4, 3, 2, 7, 1, 20, 5, 2, 8, 14, 1, 3, 21, 43, 4, 6, 3, 5, 8, 4, 9, 2, 1, 3, 1, 14, 15, 9, 30, 1, 4, 22, 7, 20, 21, 9

Offset: 1

Author

Vladimir Shevelev, May 01 2012

Keywords

• nonn

Comments

Conjecture: a(n)>0; equivalently, for every n, the arithmetic progression {6*k*n-1} contains infinitely many lessers of twin primes (A001359).

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512, A014574, A001097, A077800, A002822.

Programs

Mathematica

Table[k = 0; While[! (PrimeQ[6*k*n - 1] && PrimeQ[6*k*n + 1]), k++]; k, {n, 100}] (* T. D. Noe, May 02 2012 *)

PARI

a(n)=my(k);n*=6;until(isprime(n*k++-1)&&isprime(n*k+1),);k \\ Charles R Greathouse IV, May 01 2012