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

1,1

Comments

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

For primes x in this sequence see A143933.

Links

Table of n, a(n) for n=1..27.

Example

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.

Mathematica

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 *)

Crossrefs

Cf. A121926, A143932, A143933.

Sequence in context: A084650 A067919 A157301 * A143933 A284708 A265783

Adjacent sequences: A143928 A143929 A143930 * A143932 A143933 A143934

Keyword

nonn

Author

Artur Jasinski, Sep 05 2008

Status

approved