A091733 a(n) is the least m > 1 such that m^3 = 1 (mod n).

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

Offset: 1

Author

David Wasserman, Mar 05 2004

Keywords

• easy
• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A070667, A076947, A083501.

Programs

MATLAB

m = 2; while mod(m^3 - 1, n); m = m + 1; end; m

Maple

A:= n -> min(select(t -> type((t^3-1)/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 *)

PARI

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