A067999 -id:A067999 - cp's OEIS frontend

A091858 a(n) = n! mod prime(n).

1, 2, 1, 3, 10, 5, 8, 2, 9, 1, 22, 7, 4, 40, 29, 16, 23, 60, 48, 51, 49, 24, 74, 40, 15, 85, 3, 41, 16, 42, 119, 43, 51, 73, 14, 23, 150, 49, 104, 20, 128, 44, 185, 66, 146, 159, 178, 150, 44, 51, 48, 4, 134, 143, 118, 143, 242, 141, 149, 108, 115, 205, 306, 196, 292, 242

Offset: 1

Amarnath Murthy, Mar 13 2004

nonn

No term is 0. For positions of 1's see A067999.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Zak Seidov)

Cf. A000040, A000142, A067999.

A091858[n_] := Block[{k = p = 1, m = Prime[n]}, While[p = Mod[p k, m]; k < n, k++ ]; p]; Table[ A091858[ n], {n, 66}] (* Robert G. Wilson v, Mar 16 2004 *)
Table[Mod[n!,Prime[n]],{n,70}] (* Harvey P. Dale, Mar 01 2015 *)

Corrected and extended by Robert G. Wilson v, Mar 16 2004

A068000 Numbers k such that (k! + 1) == 0 ( mod prime(k) ).

Original entry on oeis.org

1, 2, 5, 18, 63

Offset: 1

Robert G. Wilson v, Feb 08 2002

There are no other terms below 33333. Is 63 the last term? - Hauke Worpel (hw1(AT)email.com), May 24 2003
There are no other terms below 534000. - Rick L. Shepherd, May 26 2003
There are no other terms below 10^7. - Amiram Eldar, Apr 22 2025

Cf. A067999, A066953.

Do[ If[ Mod[n! + 1, Prime[n]] == 0, Print[n]], {n, 1, 10000} ]

for(k=1, 33333, if( (k!+1)%prime(k)==0, print1(k, ", ")))

list(lim) = {my(k = 0, r = 1); forprime(p = 1, lim, k++; r *= k; if(!((r+1) % p), print1(k, ", ")));} \\ Amiram Eldar, Apr 22 2025

cp's OEIS Frontend

A091858 a(n) = n! mod prime(n).

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