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%I #16 Dec 17 2017 03:05:35
%S 2,3,13,5,31,7,55441,73,991,11,670442572801,13,2731,211,241,17,307,19,
%T 4037881,421,463,23,725902806896876799590400001,601,17551,530122321,
%U 757,29,45143585625601,31,5296855682339020801,63606090241,1123,42841
%N a(n) = smallest prime of the form n*(n+1)*(n+2)*...*(n+k) + 1, or 0 if no such prime exists.
%C a(n) = n+1 iff n+1 is prime. Conjecture: No term is zero.
%H Antti Karttunen, <a href="/A087564/b087564.txt">Table of n, a(n) for n = 1..522</a> (first 100 terms from Jean-François Alcover)
%e 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.
%p 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_
%t 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 *)
%o (PARI) for(n=1,34,k=0; m=n; while(!isprime(m+1,1),k++; m=m*(n+k)); print1(m+1,","))
%Y Cf. A087565.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Sep 15 2003
%E Edited and extended by _Klaus Brockhaus_ and _Sascha Kurz_, Sep 20 2003