A077256 -id:A077256 - cp's OEIS frontend

A077254 a(n) = prime(n)^n mod n.

0, 1, 2, 1, 1, 1, 3, 1, 8, 1, 9, 1, 2, 1, 8, 1, 8, 1, 10, 1, 13, 15, 14, 1, 7, 9, 1, 9, 22, 19, 3, 1, 26, 9, 4, 1, 9, 7, 5, 1, 15, 1, 19, 9, 17, 41, 23, 1, 31, 1, 11, 1, 29, 1, 23, 9, 8, 13, 41, 1, 39, 41, 55, 1, 53, 31, 63, 13, 8, 1, 69, 1, 2, 9, 49, 5, 16, 25, 6, 1, 80, 39, 16, 1, 29, 83

Offset: 1

Reinhard Zumkeller, Oct 31 2002

nonn

a(A077255(n)) = 1.

			a(13) = prime(13)^13 mod 13 = 41^13 mod 13 = 925103102315013629321 mod 13 = 2.

Zak Seidov, Table of n, a(n) for n = 1..10000

a(n) = A062457(n) mod n, A077256, A000040, A000027.

a:= n-> ithprime(n) &^ n mod n:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 07 2012

Table[PowerMod[Prime[n], n, n], {n, 100}] (* Zak Seidov, Dec 07 2012 *)

A077255 Numbers k such that prime(k)^k == 1 (mod k).

Original entry on oeis.org

2, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 24, 27, 32, 36, 40, 42, 48, 50, 52, 54, 60, 64, 70, 72, 80, 84, 96, 100, 105, 108, 110, 114, 120, 121, 124, 125, 126, 128, 136, 144, 148, 156, 160, 162, 168, 180, 181, 182, 189, 192, 200, 210, 216, 220, 231, 234, 240, 243, 246

Offset: 1

Reinhard Zumkeller, Oct 31 2002

nonn

Contains A023143. All terms not in A023143 are in A060679. - Robert Israel, Oct 31 2016

			prime(16)^16 mod 16 = 53^16 mod 16 = 3876269050118516845397872321 mod 16 = 1, therefore 16 is a term.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000040, A023143, A060679, A077254, A077256.

select(n -> ithprime(n) &^ n mod n = 1, [$1..1000]); # Robert Israel, Oct 31 2016

Select[Range[1000], PowerMod[Prime[#], #, #] == 1&] (* Jean-François Alcover, Dec 16 2021 *)

isok(k) = lift(Mod(prime(k), k)^k) == 1; \\ Michel Marcus, Dec 16 2021

A077254(a(n)) = 1; A077256(n) = A000040(a(n)).

cp's OEIS Frontend

A077254 a(n) = prime(n)^n mod n.

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