A067999 -id:A067999

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A091858

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

+10
3

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

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

OFFSET

1,2

COMMENTS

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

LINKS

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

MATHEMATICA

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

Table[Mod[n!, Prime[n]], {n, 70}] (* Harvey P. Dale, Mar 01 2015 *)

CROSSREFS

Cf. A000040, A000142.

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Mar 13 2004

EXTENSIONS

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

STATUS

approved

A068000

(n! + 1) == 0 ( mod prime(n) ).

+10
2

1, 2, 5, 18, 63

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

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..5.

MATHEMATICA

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

PROG

(PARI) for(X=10001, 33333, if( (X!+1)%prime(X)==0, print(X)))

CROSSREFS

Cf. A067999, A066953.

KEYWORD

nonn,hard

AUTHOR

Robert G. Wilson v, Feb 08 2002

EXTENSIONS

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

STATUS

approved

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