A087565 a(n) = smallest k such that n*(n+1)*(n+2)...(n+k) + 1 is prime, or -1 if no prime of such form exists.

0, 0, 1, 0, 1, 0, 4, 1, 2, 0, 9, 0, 2, 1, 1, 0, 1, 0, 4, 1, 1, 0, 17, 1, 2, 5, 1, 0, 8, 0, 11, 6, 1, 2, 7, 0, 73, 1, 4, 0, 1, 0, 13, 2, 5, 0, 8, 17, 2, 1, 2, 0, 2, 1, 18, 2, 1, 0, 1, 0, 2, 1, 114, 4, 5, 0, 15, 4, 1, 0, 1, 0, 4, 2, 1, 2, 1, 0, 5, 1, 5, 0, 2, 2, 9, 2, 4, 0, 1, 1, 2, 23, 7, 2, 12, 0, 12, 2, 1

Offset

1,7

Comments

a(n) = 0 iff n+1 is prime.

Since rather large numbers (up to 238 digits) are encountered in the computation, the Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3.

Links

Antti Karttunen, Table of n, a(n) for n = 1..522

Example

7+1 = 8, 7*8+1 = 57, 7*8*9+1 = 505, 7*8*9*10+1 = 5041 are all composite, but 7*8*9*10*11 + 1 = 55441 is prime, so a(7) = 4,

Mathematica

Array[If[PrimeQ@ #, 0, Block[{k = 1}, While[! PrimeQ[Pochhammer[# - 1, k + 1] + 1], k++]; k]] &, 99, 2] (* Michael De Vlieger, Dec 16 2017 *)

Prog

(PARI) for(n=1, 100, k=0; m=n; while(!isprime(m+1, 1), k++; m=m*(n+k)); print1(k, ", "))

Crossrefs

Cf. A087564, A087566.

Sequence in context: A331749 A274438 A365387 * A079163 A108536 A232631

Adjacent sequences: A087562 A087563 A087564 * A087566 A087567 A087568

Keyword

nonn

Author

Amarnath Murthy, Sep 15 2003

Extensions

Edited and extended by Klaus Brockhaus, Sep 17 2003

Escape-clause added to the definition by Antti Karttunen, Dec 16 2017

Status

approved