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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 24 22:34 EDT 2022. Contains 354047 sequences. (Running on oeis4.)