A064935 Numbers k such that (k+3)^(k+2) mod (k+1) = k.

4, 64, 376, 1188, 1468, 25804, 58588, 134944, 137344, 170584, 272608, 285388, 420208, 538732, 592408, 618448, 680704, 778804, 1163064, 1520440, 1700944, 2099200, 2831008, 4020028, 4174168, 4516108, 5059888, 5215768, 5447272

Offset: 1

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 26 2001

Keywords

• nonn

Comments

From Robert Israel, Feb 13 2025: (Start)

Numbers k such that 2^(k+2) == -1 (mod k+1).

All terms are divisible by 4.

The only term k where k+1 is prime is 4.

(End)

Examples

			(4+3)^(4+2) mod (4+1) = 7^6 mod 5 = 117649 mod 5 = 4, so 4 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..350

Crossrefs

Equals A055685(n+1) - 2.

Programs

Maple

filter:= proc(k) 2 &^(k+2) mod (k+1) = k end proc:
select(filter, [seq(i,i=4..10^7,4)]); # Robert Israel, Feb 13 2025

PARI

isok(k) = Mod(k+3, k+1)^(k+2) == k; \\ Michel Marcus, Jul 12 2021