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A238532 Number of distinct factorial numbers congruent to -1 (mod n). 2
0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 3, 0, 0, 0, 7, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Number of solutions to k! == -1 (mod n), k>=1.

Counts the frequency of the value n-1 in the n-th row of triangle A062169.

Values 1..9 occur for the first time at n = 2, 7, 23, 59, 227, 401, 71, 3643, 62939, which are all prime numbers (see also A230315). Sequence A256519 gives composite k for which a(k) > 0. - Antti Karttunen, May 24 2021

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to factorial numbers

EXAMPLE

There are two 6's in the 7th row of A062169. Therefore a(7)=2.

MAPLE

A238532 := proc(n)

    local a, k ;

    a := 0 ;

    for k from 1 to n-1 do

        if modp(k!, n) = modp(-1, n) then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc: # R. J. Mathar, Apr 02 2014

PROG

(PARI) A238532(n) = { my(m=1, s=0); for(k=1, oo, m *= k; if(!(m%n), return(s), if(1+(m%n)==n, s++))); }; \\ Antti Karttunen, May 24 2021

(PARI) A238532(n) = { my(m=Mod(1, n), s=0, x); for(k=1, oo, m *= Mod(k, n); x = lift(m); if(!x, return(s), if(x==(n-1), s++))); }; \\ (Much faster than above program) - Antti Karttunen, May 24 2021

CROSSREFS

Cf. A000142, A049046, A062169, A230315, A256519.

Sequence in context: A292261 A035153 A069847 * A097249 A112313 A297115

Adjacent sequences:  A238529 A238530 A238531 * A238533 A238534 A238535

KEYWORD

nonn

AUTHOR

R. J. Mathar, Apr 02 2014

STATUS

approved

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Last modified December 6 16:06 EST 2021. Contains 349565 sequences. (Running on oeis4.)