A077254 -id:A077254 - cp's OEIS frontend

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

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)).

A077256 Primes p such that p^k == 1 modulo k, where p=prime(k).

Original entry on oeis.org

3, 7, 11, 13, 19, 29, 37, 43, 53, 61, 71, 89, 103, 131, 151, 173, 181, 223, 229, 239, 251, 281, 311, 349, 359, 409, 433, 503, 541, 571, 593, 601, 619, 659, 661, 683, 691, 701, 719, 769, 827, 857, 911, 941, 953, 997, 1069, 1087, 1091, 1129, 1163, 1223, 1291

Offset: 1

Reinhard Zumkeller, Oct 31 2002

nonn

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

Cf. A000040, A049084, A077254, A077255.

Contains A048891.

g:= proc(t) local p; p:= ithprime(t); if p&^ t mod t = 1 then p else NULL fi end proc:
map(g, [$1..1000]); # Robert Israel, Oct 31 2016

With[{no=250}, Transpose[Select[Partition[Riffle[Prime[Range[no]], Range[no]],2], PowerMod[First[#],Last[#],Last[#]]==1&]][[1]]]  (* Harvey P. Dale, Jan 05 2011 *)
Prime[Select[Range[250], PowerMod[Prime[#],#,#]==1&]]

A077254(A049084(a(n))) = 1.

a(n) = A000040(A077255(n)).

cp's OEIS Frontend

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

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