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%I #12 Feb 17 2023 14:47:56
%S 2,2,3,11,19,31,79,209,607,1921,6337,21907,78913,295289,1143539,
%T 4574149,18859733,80014841,348776611,1559776279,7147792823,
%U 33526120127,160785623627,787685471389,3938427356623,20082117944263,104349745809077
%N a(n) is the smallest positive integer x such that x^2 - n! is prime.
%C For the smallest positive prime numbers of the form x^2 - n! see A143932.
%C For primes x in this sequence see A143933.
%e a(1)=2 because 2^2-1! = 3 is prime;
%e a(2)=2 because 2^2-2! = 2 is prime;
%e a(3)=3 because 3^2-3! = 3 is prime;
%e a(4)=11 because 11^2-4! = 97 is prime.
%t a = {}; Do[k = Round[Sqrt[n! ]] + 1; While[ ! PrimeQ[k^2 - n! ], k++ ]; AppendTo[a, k], {n, 1, 50}]; a
%t spi[n_]:=Module[{k=Ceiling[Sqrt[n!]],nf=n!},While[!PrimeQ[k^2-nf],k++];k]; Array[ spi,30] (* _Harvey P. Dale_, Feb 17 2023 *)
%Y Cf. A121926, A143932, A143933.
%K nonn
%O 1,1
%A _Artur Jasinski_, Sep 05 2008
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