

A091733


a(n) is the least m > 1 such that m^3 = 1 (mod n).


2



2, 3, 4, 5, 6, 7, 2, 9, 4, 11, 12, 13, 3, 9, 16, 17, 18, 7, 7, 21, 4, 23, 24, 25, 26, 3, 10, 9, 30, 31, 5, 33, 34, 35, 11, 13, 10, 7, 16, 41, 42, 25, 6, 45, 16, 47, 48, 49, 18, 51, 52, 9, 54, 19, 56, 9, 7, 59, 60, 61, 13, 5, 4, 65, 16, 67, 29, 69, 70, 11, 72, 25, 8, 47, 76, 45, 23, 55, 23
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OFFSET

1,1


COMMENTS

a(n) <= n + 1; the inequality is strict iff n is divisible by 9 or by a prime congruent to 1 mod 3.  Robert Israel, May 27 2014


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

a(7) = 2 because 2^3 is congruent to 1 (mod 7).


MAPLE

A:= n > min(select(t > type((t^31)/n, integer), [$2 .. n+1]));
map(A, [$1 .. 1000]); # Robert Israel, May 27 2014


MATHEMATICA

f[n_] := Block[{x = 2}, While[Mod[x^3  1, n] != 0, x++]; x]; Array[f, 79] (* Robert G. Wilson v, Mar 29 2016 *)


PROG

(MATLAB) m = 2; while mod(m^3  1, n); m = m + 1; end; m
(PARI) a(n) = my(k = 2); while(Mod(k, n)^3 != 1, k++); k; \\ Michel Marcus, Mar 30 2016


CROSSREFS

Cf. A070667, A076947, A083501.
Sequence in context: A173527 A043267 A167514 * A066990 A097449 A104415
Adjacent sequences: A091730 A091731 A091732 * A091734 A091735 A091736


KEYWORD

easy,nonn


AUTHOR

David Wasserman, Mar 05 2004


STATUS

approved



