A262207 a(n) = prime(n)^n mod n^n.

0, 1, 17, 97, 1676, 21241, 214259, 5020449, 34808102, 7233300201, 46070142226, 7806783217105, 165239209697109, 1608006723911113, 48560388990668468, 4867006141797699265, 530779430908845468654, 18442832496573633213385

Offset: 1

Author

Altug Alkan, Sep 15 2015

Keywords

• nonn
• easy

Comments

Inspired by A002380, A067602, A138654.

a(3), a(4), a(7) and a(48) are prime numbers.

There are no further prime numbers up to a(1000). - Harvey P. Dale, Jun 15 2025

Examples

			For n = 1, a(n) = prime(1)^1 mod 1^1 = 2^1 mod 1 = 2 mod 1 = 0.
For n = 2, a(n) = prime(2)^2 mod 2^2 = 3^2 mod 4 = 9 mod 4 = 1.
For n = 3, a(n) = prime(3)^3 mod 3^3 = 5^3 mod 27 = 125 mod 27 = 17.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A002380, A067602, A138654, A000312, A062457, A121623.

Programs

Mathematica

Table[Mod[Prime[n]^n, n^n], {n, 18}] (* Michael De Vlieger, Sep 15 2015 *)
Table[PowerMod[Prime[n],n,n^n],{n,20}] (* Harvey P. Dale, Jun 15 2025 *)

PARI

a(n) = (prime(n)^n) % (n^n);
vector(18, n, a(n))

Formula

a(n) = A062457(n) mod A000312(n). - Michel Marcus, Sep 15 2015