A143931 -id:A143931 - cp's OEIS frontend

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

Offset: 1

Artur Jasinski, Sep 05 2008

nonn

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.

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

Cf. A121926, A143931, A143932.

f:= proc(n) local p,t;
  t:= n!;
  p:= floor(sqrt(t));
  do
    p:= nextprime(p);
    if isprime(p^2-t) then return p fi
  od
end proc:
map(f, [$1..28]); # Robert Israel, Feb 10 2019

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 *)

a(n)=my(N=n!,x=sqrtint(N)+1); while(!isprime(x^2-N), x=nextprime(x+1)); x \\ Charles R Greathouse IV, Dec 09 2014

Corrected by Charles R Greathouse IV, Dec 09 2014

A143932 a(n) = smallest positive prime number of the form x^2 - n! (where x is a positive integer).

Original entry on oeis.org

3, 2, 3, 97, 241, 241, 1201, 3361, 5569, 61441, 240769, 915049, 240769, 17302321, 7076521, 49186201, 2100735289, 1074527281, 23971813321, 32354445841, 68820869329, 2992426816129, 26238323995129, 104071698229321

Offset: 1

Artur Jasinski, Sep 05 2008

nonn

For smallest positive integers x see A143931. Prime x see A143933.

			a(1)=3 because 2^2 - 1! = 3;
a(2)=2 because 2^2 - 2! = 2;
a(3)=3 because 3^2 - 3! = 3;
a(4)=97 because 11^2 - 4! = 97.

Cf. A121926, A143931, A143933.

b = {}; Do[k = Round[Sqrt[n! ]] + 1; While[ ! PrimeQ[k^2 - n! ], k++ ]; AppendTo[b, k^2-n! ], {n, 1, 50}]; b

cp's OEIS Frontend

A143933 a(n) is the smallest prime x such that x^2-n! is also prime.

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