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A192419 Smallest k such that 1^3, 2^3, 3^3,... n^3 are distinct modulo k. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A214881 A163831 A326399 * A081836 A263721 A154290

Adjacent sequences:  A192416 A192417 A192418 * A192420 A192421 A192422

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jun 30 2011

STATUS

approved

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Last modified November 21 11:35 EST 2019. Contains 329370 sequences. (Running on oeis4.)