A154664 Numbers k such that k!^2 + 7493 and abs(k!^2 - 7493) are primes.

3, 4, 5, 6, 12

Offset

1,1

Comments

Next term is larger than 72.

Next term is larger than 1000. - Harvey P. Dale, Feb 03 2016

There are no more terms: none were found in a search past 7493 and (k!)^2 + 7493 is divisible by 7493 for all k >= 7493. - Michael S. Branicky, May 18 2026

Links

Table of n, a(n) for n=1..5.

Mathematica

lst={}; a=7493; Do[If[PrimeQ[n!^2-a]&&PrimeQ[n!^2+a], AppendTo[lst, n]], {n, 3*4!}]; lst
Select[Range[20], AllTrue[(#!)^2+{7493, -7493}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 03 2016 *)

Crossrefs

Cf. A144046, A154660, A154661, A154662, A154663.

Sequence in context: A356050 A299299 A103402 * A371242 A380090 A385043

Adjacent sequences: A154661 A154662 A154663 * A154665 A154666 A154667

Keyword

nonn,fini,full

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Extensions

Definition corrected by Georg Fischer, May 18 2026

Status

approved