A245085 - OEIS

%I #47 Dec 18 2014 02:13:34

%S 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,

%T 23,11,11,18,17,17,18,21,15,14,28,13,26,36,8,13,32,22,16,6,24,15,22,

%U 28,21,15,28,16,42,23,32,25,8,20,18,20,33,26,10,35,14,5,29

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

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

%C See comments in A247190.

%H Peter J. C. Moses and Chai Wah Wu, <a href="/A245085/b245085.txt">Table of n, a(n) for n = 3..10002</a> First 1000 terms from Peter J. C. Moses.

%F a(n) >= A247190(n).

%t Table[ans={};

%t 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 *)

%o (Python)

%o from sympy import prime

%o def A245085(n):

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

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

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

%o ........if f in fv:

%o ............return i-1

%o ........else:

%o ............fv[f] = i

%o ....return p-1 # _Chai Wah Wu_, Dec 15 2014

%Y Cf. A000040, A247190.

%K nonn

%O 3,1

%A _Vladimir Shevelev_, Nov 25 2014

%E More terms from _Peter J. C. Moses_, Nov 25 2014