A077256 -id:A077256

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A077254

Prime(n)^n mod n.

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

a(A077255(n)) = 1.

LINKS

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

EXAMPLE

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

MAPLE

a:= n-> ithprime(n) &^ n mod n:

seq(a(n), n=1..100); # Alois P. Heinz, Dec 07 2012

MATHEMATICA

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 31 2002

STATUS

approved

A077255

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

MAPLE

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

MATHEMATICA

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

PROG

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