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%I #30 Dec 15 2017 17:36:06
%S 1,1,1,1,1,4,8,11,4,11,1,4,7,6,14,3,5,2,7,3,6,20,2,9,20,2,5,7,31,2,12,
%T 13,24,7,39,21,35,24,22,3,21,8,9,13,39,21,29,10,3,62,52,21,3,36,28,15,
%U 18,33,7,46,33,20,14,22,41,7,27,39,20,4,4,5,15,27,1,44,99,9,52,2,27,12
%N Smallest k such that k*prime(n)# + 1 is prime where prime(n)# is the n-th primorial number A002110(n).
%C From _Pierre CAMI_, Sep 12 2017: (Start)
%C Conjectures:
%C lim_{N->inf} (Sum_{n=1..N} a(n)) / (Sum_{n=1..N} n) = 1/2;
%C a(n)/n is always < 4.
%C This is certified for the first 3100 primes a(n)*prime(n)#+1.
%C (End)
%H Pierre CAMI, <a href="/A076689/b076689.txt">Table of n, a(n) for n = 1..3100</a>
%H Pierre CAMI, <a href="/A076689/a076689.txt">PFGW Sript</a>
%t With[{P = FoldList[Times, Prime@ Range@ 120]}, Table[k = 1; While[CompositeQ[k P[[n]] + 1], k++]; k, {n, Length@ P}]] (* _Michael De Vlieger_, Sep 18 2017 *)
%o (PARI) a(n) = my(k=1, pr = prod(i=1, n, prime(i))); while (! isprime(k*pr+1), k++); k; \\ _Michel Marcus_, Oct 09 2017
%Y Cf. A014545 (n for which k=1), A073917 (the primes).
%K nonn
%O 1,6
%A _Jason Earls_, Nov 10 2002
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