A225944 -id:A225944 - cp's OEIS frontend

A177005 Numbers k such that k^k = k (mod prime(k)).

1, 4, 169, 391, 1546, 16761, 18278, 20201, 21775, 31120, 126882, 178465, 9502273, 10553442, 24677776, 56923413, 422766345, 1759518201, 4152696703, 6800832991, 14421293461, 106195400697, 667339219893, 915091102299

Offset: 1

Farideh Firoozbakht, May 02 2010

20201 is a prime term of this sequence. What is the next such prime?

The next prime term is a(20) = 6800832991. - Giovanni Resta, May 10 2020

Cf. A117131, A225944.

Do[If[PowerMod[n, n, Prime[n]] == n, Print[n]], {n, 350000000}]

is(k) = Mod(k, prime(k))^k == k; \\ Jinyuan Wang, May 09 2020

a(17) from Jinyuan Wang, May 09 2020

a(18)-a(24) from Giovanni Resta, May 10 2020

A225945 Numbers k such that prime(k) divides k^k + 1.

Original entry on oeis.org

1, 6, 60, 136, 124796, 3919272, 18363918, 153037808, 965108649, 3140421892, 5961162423, 20437804784

Offset: 1

Alex Ratushnyak, May 21 2013

a(12) > 2*10^10. - Giovanni Resta, May 23 2013

Cf. A000040, A000312, A014566, A225944.

Select[Range[10^6], (p = Prime[#]; PowerMod[#, #, p] == p - 1) &] (* Giovanni Resta, May 23 2013 *)

from sympy import nextprime, prime
from itertools import count, islice
def agen(startn=1): # generator of terms
    pn = prime(startn)
    for n in count(startn):
        if pow(n, n, pn) == pn - 1:
            yield n
        pn = nextprime(pn)
print(list(islice(agen(), 5))) # Michael S. Branicky, May 25 2023

a(6)-a(11) from Giovanni Resta, May 23 2013

a(12) from Michael S. Branicky, May 25 2023

cp's OEIS Frontend

A177005 Numbers k such that k^k = k (mod prime(k)).

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