A192419 Smallest k such that 1^3, 2^3, 3^3,... n^3 are distinct modulo k.

1, 2, 3, 5, 5, 6, 10, 10, 10, 10, 11, 15, 15, 15, 15, 17, 17, 22, 22, 22, 22, 22, 23, 29, 29, 29, 29, 29, 29, 30, 33, 33, 33, 34, 41, 41, 41, 41, 41, 41, 41, 46, 46, 46, 46, 46, 47, 51, 51, 51, 51, 53, 53, 55, 55, 58, 58, 58, 59, 66, 66, 66, 66, 66, 66, 66, 69, 69, 69, 71, 71, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82

Offset

1,2

Comments

The discriminator D(3,n).

It appears that a(n) ~ n. Is there an explicit formula as for A016726? - M. F. Hasler, May 04 2016

Links

Harvey P. Dale, 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

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:
A192419 := proc(n) dis(3, n) ; end proc:

Mathematica

dmk[n_]:=Module[{k=1, res}, While[res=Table[PowerMod[i, 3, k], {i, n}]; Length[ res]!= Length[Union[res]], k++]; k]; Array[dmk, 90] (* Harvey P. Dale, Jan 28 2013 *)

Prog

(PARI) A192419(nMax)={my(S=[], a=1); vector(nMax, n, S=concat(S, n^3); while(#Set(S%a)<n, a++); a)} \\ M. F. Hasler, May 04 2016

Crossrefs

Cf. A016726, A192420.

Sequence in context: A364085 A163831 A326399 * A081836 A263721 A351259

Adjacent sequences: A192416 A192417 A192418 * A192420 A192421 A192422

Keyword

nonn

Author

R. J. Mathar, Jun 30 2011

Status

approved