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A245085 Maximal t in [2, prime(n)-1] such that all the smallest positive residues of 2!,3!,...,t! modulo prime(n) are distinct. 2
4, 5, 3, 8, 5, 4, 7, 5, 9, 12, 6, 10, 9, 11, 4, 15, 7, 8, 7, 13, 18, 9, 18, 13, 17, 9, 10, 10, 23, 11, 11, 18, 17, 17, 18, 21, 15, 14, 28, 13, 26, 36, 8, 13, 32, 22, 16, 6, 24, 15, 22, 28, 21, 15, 28, 16, 42, 23, 32, 25, 8, 20, 18, 20, 33, 26, 10, 35, 14, 5, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

a(n) = prime(n)-1, if A247190(n)=0; else a(n) = m-1, where m is defined in A247190.

See comments in A247190.

LINKS

Peter J. C. Moses and Chai Wah Wu, Table of n, a(n) for n = 3..10002 First 1000 terms from Peter J. C. Moses.

FORMULA

a(n) >= A247190(n).

MATHEMATICA

Table[ans={};

NestWhile[#+1&, 2, (AppendTo[ans, Mod[#!, Prime[n]]]; (Length[ans]<Prime[n]-1)&&(Max[Last[Transpose[Tally[ans]]]]==1))&]-1, {n, 3, 50}] (* Peter J. C. Moses, Nov 25 2014 *)

PROG

(Python)

from sympy import prime

def A245085(n):

....p, f, fv = prime(n), 1, {}

....for i in range(2, p):

........f = (f*i) % p

........if f in fv:

............return i-1

........else:

............fv[f] = i

....return p-1 # Chai Wah Wu, Dec 15 2014

CROSSREFS

Cf. A000040, A247190.

Sequence in context: A004493 A328238 A170929 * A299420 A019836 A020503

Adjacent sequences:  A245082 A245083 A245084 * A245086 A245087 A245088

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Nov 25 2014

EXTENSIONS

More terms from Peter J. C. Moses, Nov 25 2014

STATUS

approved

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)