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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

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OFFSET

1,3

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

PROG

(PARI) a(n) = (prime(n)^n) % (n^n);

vector(18, n, a(n))

CROSSREFS

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

Sequence in context: A184327 A331877 A358572 * A282997 A231667 A044268

Adjacent sequences: A262204 A262205 A262206 * A262208 A262209 A262210

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Sep 15 2015

STATUS

approved

URL: https://oeis.org/A262207

⇱ A262207 - OEIS