A073688 Group the natural numbers so that the product of the terms in each group + 1 is a prime: (1), (2), (3, 4), (5, 6), (7, 8, 9, 10, 11), (12), (13, 14, 15), (16), ... This is the sequence of such primes.

2, 3, 13, 31, 55441, 13, 2731, 17, 307, 4037881, 601, 530122321, 63606090241, 115511761, 91081, 2307336935904001, 185137, 3541, 238267, 1250895361, 4831, 5113, 2370937801, 79, 292666711681, 32808912827897606401

Offset

0,1

Comments

No group can contain 4 terms as the product of four consecutive integers + 1 is a square. Question: are there other numbers like 4, which always give a composite number?

Links

Table of n, a(n) for n=0..25.

Mathematica

t = {}; s = 1; Do[s = s*i; If[PrimeQ[s + 1], AppendTo[t, s + 1]; s = 1], {i, 100}]; t (* Jayanta Basu, Jul 07 2013 *)

Crossrefs

Cf. A073689, A073690.

Sequence in context: A296291 A072997 A037428 * A299967 A216359 A169983

Adjacent sequences: A073685 A073686 A073687 * A073689 A073690 A073691

Keyword

nonn

Author

Amarnath Murthy, Aug 12 2002

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 24 2003

Status

approved