A154665 Numbers k such that k!^2 + 8663 and abs(k!^2 - 8663) are primes.

3, 4, 5, 6, 40

Offset

1,1

Comments

Next term is larger than 72.

a(6) > 1000 (if it exists) - Robert Price, Mar 26 2019

There are no more terms: none were found in a search past 8663 and (k!)^2 + 8663 is divisible by 8663 for all k >= 8663. - Michael S. Branicky, May 19 2026

Links

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

Mathematica

lst={}; a=8663; Do[If[PrimeQ[n!^2-a]&&PrimeQ[n!^2+a], AppendTo[lst, n]], {n, 3*4!}]; lst

Crossrefs

Cf. A144046, A154660, A154661, A154662, A154663, A154664.

Sequence in context: A083401 A281829 A083400 * A056190 A202702 A388178

Adjacent sequences: A154662 A154663 A154664 * A154666 A154667 A154668

Keyword

nonn,fini,full

Author

Vladimir Joseph Stephan Orlovsky, Jan 13 2009

Extensions

Definition corrected by Georg Fischer, May 18 2026

Status

approved