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A295741 a(n) is smallest divisor d of the n-th primorial such that d + prime(n)#/d is prime.

%I A295741 #20 Jan 02 2018 20:33:26
%S A295741 1,1,1,1,1,1,2,5,6,10,2,1,2,11,7,2,41,2,5,5,5,3,51,10,3,14,37,10,7,2,
%T A295741 17,17,62,21,3,38,17,47,13,17,13,7,21,83,10,138,10,26,2,7,19,31,15,13,
%U A295741 5,23,103,19,5,95,61,6,15,2,35,13,19,65,39,7,43,73,13,26,97,1,91,2,78,19,39,34,167,82,10,38,66,58,2,46,71
%N A295741 a(n) is smallest divisor d of the n-th primorial such that d + prime(n)#/d is prime.
%C A295741 Conjecture: a(n) < prime(n)^2 for n > 0.
%C A295741 a(n) = 1 iff n belongs to A014545.
%C A295741 Inspired by A293756.
%H A295741 Robert G. Wilson v, <a href="/A295741/b295741.txt">Table of n, a(n) for n = 0..1000</a>
%e A295741 a(3) = 1 because 1 + prime(3)#/1 = 1 + 2*3*5 = 31 and 31 is a prime;
%e A295741 a(6) = 2 because 2 + prime(6)#/2 = 2 + 2*3*5*7*11*13/2 = 15017 and that is a prime;
%e A295741 a(7) = 5 because 5 + prime(7)#/5 = 5 + 2*3*5*7*11*13*17/5 = 102107 which is a prime; etc.
%t A295741 f[n_] := Block[{d = 1, p = Fold[Times, 1, Prime@ Range@ n]}, While[ !PrimeQ[d + p/d], d++]; d]; Array[f, 90]
%o A295741 (PARI) a(n)=my(P=vecprod(primes(n))); for(d=1,P, if(P%d==0 && ispseudoprime(d+P/d), return(d))) \\ _Charles R Greathouse IV_, Nov 27 2017
%Y A295741 Cf. A002110, A005235, A014545.
%K A295741 nonn
%O A295741 0,7
%A A295741 _Thomas Ordowski_ and _Robert G. Wilson v_, Nov 26 2017