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%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
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