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

1,1

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).

Links

Table of n, a(n) for n=1..16.

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A007528, A057130.

Sequence in context: A142380 A042632 A107966 * A160442 A125417 A156640

Adjacent sequences: A057128 A057129 A057130 * A057132 A057133 A057134

Keyword

nonn,easy

Author

Henry Bottomley, Aug 11 2000

Extensions

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

More terms from Michel Marcus, Sep 08 2013

Status

approved