A143933 -id:A143933

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A143931

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn

AUTHOR

Artur Jasinski, Sep 05 2008

STATUS

approved

A143932

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

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.