A089305 - OEIS

%I #14 Jul 29 2017 01:10:05

%S 3,7,13,604801,31,43,55441,73,991,1321,670442572801,157,2731,211,241,

%T 39070081,307,6841,4037881,421,463,173059286401,

%U 725902806896876799590400001,601,17551,530122321,757,24165121,45143585625601,29761,5296855682339020801,63606090241,1123,42841,4758977059201

%N 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.

%C Conjecture: No entry is zero.

%e a(1) = 1*2 + 1 = 3 and not 2.

%e 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.

%p 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_

%t 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 *)

%Y Cf. A087564.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Nov 01 2003

%E More terms from _Jim Nastos_, Nov 02 2003

%E More terms from _David Wasserman_, Sep 09 2005