A245085 Maximal t in [2, prime(n)-1] such that all the smallest positive residues of 2!,3!,...,t! modulo prime(n) are distinct.

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

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: A348051 A328238 A170929 * A299420 A019836 A353314

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