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

%I #6 Sep 08 2013 02:55:39

%S 29,329,5609,129029,3741869,153416669,7210583489,382160924969,

%T 22547494573229,1600872114699329,132872385520044389,

%U 11825642311283950709,1194389873439679021709,127799716458045655322969,14441367959759159051495609,1891819202728449835745924909

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

%C 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).

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

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

%o (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

%Y Cf. A007528, A057130.

%K nonn,easy

%O 1,1

%A _Henry Bottomley_, Aug 11 2000

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

%E More terms from _Michel Marcus_, Sep 08 2013

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Last modified November 29 13:27 EST 2023. Contains 367445 sequences. (Running on oeis4.)