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a(n) is the smallest positive k such that n!*prime(n) + k is a prime.
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%I #20 Aug 13 2021 10:18:02

%S 1,1,1,5,1,11,11,11,1,11,23,43,19,41,17,29,1,19,71,157,1,23,79,67,47,

%T 53,37,53,31,67,73,223,307,67,1,197,151,43,43,157,89,137,47,127,173,

%U 97,89,79,223,79,83,151,163,89,167,313,179,101,127,101,181,193,421,73

%N a(n) is the smallest positive k such that n!*prime(n) + k is a prime.

%C k equals nextprime(n!*prime(n)) - n!*prime(n).

%F a(n) = A151800(n!*prime(n)) - n!*prime(n).

%t spk[n_]:=Module[{c=n!Prime[n]},NextPrime[c]-c]; Array[spk,70] (* _Harvey P. Dale_, Aug 13 2021 *)

%o (PARI) a(n) = my(x=n!*prime(n)); nextprime(x+1) - x; \\ _Michel Marcus_, Feb 22 2020

%Y Cf. A000040, A000142, A151800, A332731.

%K nonn

%O 1,4

%A _Mohamed Sami Gattoufi_, Feb 21 2020