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A061007 a(n) = -(n-1)! mod n. 9
0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The following sequences all appear to have the same parity (with an extra zero term at the start of A010051): A010051, A061007, A035026, A069754, A071574. - Jeremy Gardiner, Aug 09 2002

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(4) = 2, a(p) = 1 for p prime, a(n) = 0 otherwise. Apart from n = 4, a(n) = A010051(n) = A061006(n)/(n-1).

EXAMPLE

a(4) = 2 since -(4 - 1)! = -6 = 2 mod 4.

a(5) = 1 since -(5 - 1)! = -24 = 1 mod 5.

a(6) = 0 since -(6 - 1)! = -120 = 0 mod 6.

MAPLE

P=proc(n) local a, i, k, w; print(0); for i from 0 by 1 to n do w:=(i! mod (i+2)); print(w); od; end: P(1000); # Paolo P. Lava, Apr 23 2007

MATHEMATICA

Table[Mod[-(n - 1)!, n], {n, 100}] (* Alonso del Arte, Mar 20 2014 *)

PROG

(PARI) A061007(n) = ((-((n-1)!))%n); \\ Antti Karttunen, Aug 27 2017

CROSSREFS

Positive for all but the first term of A046022.

Cf. A000040, A000142, A010051, A055976, A061006, A061008, A061009.

Sequence in context: A116852 A269245 A060154 * A060838 A206567 A085252

Adjacent sequences:  A061004 A061005 A061006 * A061008 A061009 A061010

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Apr 12 2001

STATUS

approved

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Last modified January 22 08:58 EST 2018. Contains 298042 sequences.