A089305 Smallest prime of the form n*(n+1)*(n+2)...(n+k) + 1, k > 0, i.e., a(n) > n+1, or 0 if no such prime exists.

3, 7, 13, 604801, 31, 43, 55441, 73, 991, 1321, 670442572801, 157, 2731, 211, 241, 39070081, 307, 6841, 4037881, 421, 463, 173059286401, 725902806896876799590400001, 601, 17551, 530122321, 757, 24165121, 45143585625601, 29761, 5296855682339020801, 63606090241, 1123, 42841, 4758977059201

Offset

1,1

Comments

Conjecture: No entry is zero.

Links

Table of n, a(n) for n=1..35.

Example

a(1) = 1*2 + 1 = 3 and not 2.
a(4) = 604801 = 4*5*6*7*8*9*10 + 1 and 4*5 + 1, 4*5*6 + 1, etc. up to 4*5*...*9 + 1 are composite.

Maple

for i from 2 while i < 40 do c := i; for j from i+1 while j < 10000000 do c := c*j; if (isprime(c+1)) then print(i, j, c+1); break; end if; end do; end do; # Jim Nastos

Mathematica

sp[n_]:=Module[{k=1}, While[!PrimeQ[Times@@Range[n, n+k]+1], k++]; Times@@ Range[ n, n+k]+1]; Array[sp, 40] (* Harvey P. Dale, Jun 17 2014 *)

Crossrefs

Cf. A087564.

Sequence in context: A135623 A172291 A343589 * A112618 A058027 A128661

Adjacent sequences: A089302 A089303 A089304 * A089306 A089307 A089308

Keyword

nonn

Author

Amarnath Murthy, Nov 01 2003

Extensions

More terms from Jim Nastos, Nov 02 2003

More terms from David Wasserman, Sep 09 2005

Status

approved