A087564 a(n) = smallest prime of the form n*(n+1)*(n+2)*...*(n+k) + 1, or 0 if no such prime exists.

2, 3, 13, 5, 31, 7, 55441, 73, 991, 11, 670442572801, 13, 2731, 211, 241, 17, 307, 19, 4037881, 421, 463, 23, 725902806896876799590400001, 601, 17551, 530122321, 757, 29, 45143585625601, 31, 5296855682339020801, 63606090241, 1123, 42841

Offset

1,1

Comments

a(n) = n+1 iff n+1 is prime. Conjecture: No term is zero.

Links

Antti Karttunen, Table of n, a(n) for n = 1..522 (first 100 terms from Jean-François Alcover)

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) = 55441.

Maple

for n from 1 to 70 do k := 0: while(not isprime(1+product(n+i, i=0..k ))) do k := k+1:od:a[n] := 1+product(n+i, i=0..k):od:seq(a[l], l=1..70); # Sascha Kurz

Mathematica

kmax = 120; a[n_] := For[k = 0, True, k++, If[k == kmax, Return[0], If[PrimeQ[p = Pochhammer[n, k+1] + 1], Return[p]]]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 02 2013 *)

Prog

(PARI) for(n=1, 34, k=0; m=n; while(!isprime(m+1, 1), k++; m=m*(n+k)); print1(m+1, ", "))

Crossrefs

Cf. A087565.

Sequence in context: A076988 A128369 A087568 * A306431 A192362 A057776

Adjacent sequences: A087561 A087562 A087563 * A087565 A087566 A087567

Keyword

nonn

Author

Amarnath Murthy, Sep 15 2003

Extensions

Edited and extended by Klaus Brockhaus and Sascha Kurz, Sep 20 2003

Status

approved