A073690 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 the number of terms in each group.

1, 1, 2, 2, 5, 1, 3, 1, 2, 5, 2, 6, 7, 5, 3, 9, 3, 2, 3, 5, 2, 2, 5, 1, 6, 10, 13, 1, 11, 8, 3, 2, 3, 1, 7, 7, 18, 43, 7, 6, 7, 1, 27, 16, 1, 7, 6, 2, 1, 2, 16, 6, 9, 3, 2, 24, 3, 1, 6, 8, 6, 8, 6, 19, 6, 1, 12, 5, 7, 13, 1, 7, 3, 7, 6, 6, 1, 7, 20, 20, 20, 2, 1, 5, 1, 10, 3, 1, 7, 2, 1, 13, 1, 9, 9

Offset

0,3

Comments

4 cannot be a member. Do all other positive integers occur?

Links

Table of n, a(n) for n=0..94.

Mathematica

t = {}; s = 1; c = 0; Do[s = s*i; c += 1; If[PrimeQ[s + 1], AppendTo[t, c]; s = 1; c = 0], {i, 630}]; t (* Jayanta Basu, Jul 07 2013 *)

Crossrefs

Cf. A073688, A073689.

Sequence in context: A267857 A173169 A016586 * A079301 A079300 A128932

Adjacent sequences: A073687 A073688 A073689 * A073691 A073692 A073693

Keyword

nonn

Author

Amarnath Murthy, Aug 12 2002

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 24 2003 and Dean Hickerson, Apr 27 2003

Status

approved