A049579 Numbers k such that prime(k)+2 divides (prime(k)-1)!.

4, 6, 8, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 42, 44, 46, 47, 48, 50, 51, 53, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95

Offset

1,1

Comments

Numbers k such that prime(k+1) - prime(k) does not divide prime(k+1) + prime(k). These are the numbers k for which prime(k+1) - prime(k) > 2. - Thomas Ordowski, Mar 31 2022

Links

Table of n, a(n) for n=1..70.

Example

prime(4)=7, 6!+1=721 gives residue 1 if divided by prime(4)+2=9.

Mathematica

pnmQ[n_]:=Module[{p=Prime[n]}, Mod[(p-1)!+1, p+2]==1]; Select[Range[ 100], pnmQ] (* Harvey P. Dale, Jun 24 2017 *)

Prog

(PARI) isok(n) = (((prime(n)-1)! + 1) % (prime(n)+2)) == 1; \\ Michel Marcus, Dec 31 2013

Crossrefs

Sequence in context: A211302 A123938 A121150 * A137242 A098015 A180638

Adjacent sequences: A049576 A049577 A049578 * A049580 A049581 A049582

Keyword

nonn

Author

Labos Elemer

Extensions

Definition edited by Thomas Ordowski, Mar 31 2022

Status

approved