A143933 - OEIS

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A143933

a(n) is the smallest prime x such that x^2-n! is also prime.

2, 2, 3, 11, 19, 31, 79, 211, 607, 1931, 6337, 21961, 78919, 295291, 1143563, 4574149, 18859777, 80014843, 348776611, 1559776279, 7147792903, 33526120129, 160785623729, 787685471519, 3938427356629, 20082117944579, 104349745809137, 552166953567737

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OFFSET

1,1

COMMENTS

Every prime > 3 in this sequence is bigger than the n-th prime, see comment to A121926. For the smallest number x such that x^2-n! is prime see A143931. For the smallest prime numbers of the form x^2-n! see A143932.

LINKS

Robert Israel, Table of n, a(n) for n = 1..300

MAPLE

f:= proc(n) local p, t;

t:= n!;

p:= floor(sqrt(t));

p:= nextprime(p);

if isprime(p^2-t) then return p fi

end proc:

map(f, [$1..28]); # Robert Israel, Feb 10 2019

MATHEMATICA

f[n_] := Block[{p = NextPrime[ Sqrt[ n!]]}, While[ !PrimeQ[p^2 - n!], p = NextPrime@ p]; p]; Array[f, 27] (* Robert G. Wilson v, Jan 08 2015 *)