A143933 -id:A143933 - cp's OEIS frontend

A143931 a(n) is the smallest positive integer x such that x^2 - n! is prime.

2, 2, 3, 11, 19, 31, 79, 209, 607, 1921, 6337, 21907, 78913, 295289, 1143539, 4574149, 18859733, 80014841, 348776611, 1559776279, 7147792823, 33526120127, 160785623627, 787685471389, 3938427356623, 20082117944263, 104349745809077

Offset: 1

Artur Jasinski, Sep 05 2008

nonn

For the smallest positive prime numbers of the form x^2 - n! see A143932.

For primes x in this sequence see A143933.

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

Cf. A121926, A143932, A143933.

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

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

A143931 a(n) is the smallest positive integer x such that x^2 - n! is prime.

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