A057131 One less than six times product of first n primes of form 6k-1.

29, 329, 5609, 129029, 3741869, 153416669, 7210583489, 382160924969, 22547494573229, 1600872114699329, 132872385520044389, 11825642311283950709, 1194389873439679021709, 127799716458045655322969, 14441367959759159051495609, 1891819202728449835745924909

Offset: 1

Author

Henry Bottomley, Aug 11 2000

Keywords

• nonn
• easy

Comments

a(n)=5 mod 6, so a(n) has at least one prime factor of form 6k-1 and this is not one of those included in the calculation of a(n); for example 5609 has 71 as a prime factor. Therefore there are an infinite number of prime numbers of form 6k-1 (and also of form 3k-1).

Examples

			a(3) = 6*(5*11*17)-1 = 5609.
		

Crossrefs

Cf. A007528, A057130.

Programs

PARI

lista(nn) = {pp = 6; for (n = 1, nn, p = prime(n); if (Mod(p, 6) == -1, pp *= p; print1(pp-1, ", ")););} \\ Michel Marcus, Sep 08 2013

Formula

a(n) = (a(n-1)+1)*A007528(n)-1 = 6*A057130(n)-1.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Oct 06 2000

More terms from Michel Marcus, Sep 08 2013