A045924 Numbers n such that prime(n) == -1 (mod n).

1, 2, 3, 4, 10, 70, 72, 182, 440, 1053, 6458, 6461, 6471, 40087, 40089, 251737, 251742, 637320, 637334, 637336, 1617173, 4124466, 10553445, 10553455, 10553569, 10553570, 10553574, 10553576, 10553819, 10553829, 27067100, 27067262, 69709705, 69709719, 69709734, 69709873

Offset: 1

Author

Len Smiley

Keywords

• nonn

Comments

Same as n such that n divides A008864(n). - David James Sycamore, Jul 23 2018

Also numbers n such that prime(n) == n-1 (mod n). - Muniru A Asiru, Jul 24 2018

Examples

			10 is a member because the 10th prime, 29, is congruent to -1 mod 10.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..108
• E. Labos, Graph of prime(n) mod n

Crossrefs

Cf. A004648 and esp. A023143.

Cf. A052013, A048891, A092044, A092045, A092046, A092047, A092048, A092049, A092050, A092051, A092052, A008864.

Programs

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = 1; Do[ If[Mod[p = NextPrim[p], n] == n - 1, Print[n]], {n, 1, 10^9}] (* Robert G. Wilson v, Feb 18 2004 *)

PARI

isok(n) = Mod(prime(n), n) == -1; \\ Michel Marcus, Jul 24 2018

Extensions

More terms from Patrick De Geest, Nov 15 1999

Terms a(33) and beyond from Giovanni Resta, Feb 23 2020