A192420 Smallest k such that 1^4, 2^4, 3^4,... ,n^4 are distinct modulo k.

1, 2, 6, 9, 11, 14, 14, 18, 19, 22, 22, 31, 31, 31, 31, 38, 38, 38, 38, 43, 43, 46, 46, 59, 59, 59, 59, 59, 59, 62, 62, 67, 67, 71, 71, 79, 79, 79, 79, 83, 83, 86, 86, 94, 94, 94, 94, 103, 103, 103, 103, 107, 107, 118, 118, 118, 118, 118, 118, 127, 127, 127, 127, 131, 131, 134, 134, 139, 139

Offset: 1

Author

R. J. Mathar, Jun 30 2011

Keywords

• nonn

Comments

The discriminator D(4,n).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• P. Moree, H. Roskam, On an arithmetical function related to Euler's totient and the discriminator, Fib. Quart. 33 (4) (1995), 332-340

Crossrefs

Cf. A016726, A192419.

Programs

Maple

dis := proc(j,n) local k,s,i; for k from 1 do s := {} ; for i from 1 to n do s := s union { (i^j) mod k} ; end do: if nops(s) = n then return k; end if; end do: end proc:
A192420 := proc(n) dis(4,n) ; end proc:

Mathematica

a[n_] := For[k = 1, True, k++, If[Unequal @@ PowerMod[Range[n], 4, k], Return[k]]]; Array[a, 100] (* Jean-François Alcover, May 18 2018 *)

PARI

A192420(nMax,f=n->n^4)={my(S=[],a=1); vector(nMax,n,S=concat(S,f(n));while(#Set(S%a)M. F. Hasler, May 04 2016