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A003570
For n>0, a(n) = least positive number m such that 8^m == +1 or -1 (mod 2n + 1), with a(0) = 0 by convention.
0
0, 1, 2, 1, 1, 5, 2, 4, 4, 3, 2, 11, 10, 3, 14, 5, 5, 4, 6, 4, 10, 7, 4, 23, 7, 8, 26, 20, 3, 29, 10, 2, 2, 11, 22, 35, 3, 20, 10, 13, 9, 41, 8, 28, 11, 4, 10, 12, 8, 5, 50, 17, 4, 53, 6, 12, 14, 44, 4, 8, 55, 20, 50, 7, 7, 65, 6, 12, 34, 23, 46, 20, 14, 14, 74, 5, 8, 20, 26, 52, 11, 27, 20, 83
OFFSET
0,3
COMMENTS
Multiplicative suborder of 8 (mod 2n+1) = sord(8, 2n+1). - Harry J. Smith, Feb 11 2005
REFERENCES
H. Cohen, Course in Computational Algebraic Number Theory, Springer, 1993, p. 25, Algorithm 1.4.3
LINKS
Eric Weisstein's World of Mathematics, Multiplicative Order.
EXAMPLE
a(1) = 1 since 8^1 = 8 == -1 (mod 3).
a(2) = 2 since 8^2 = 64 == -1 (mod 5).
MATHEMATICA
Suborder[k_, n_] := If[n > 1 && GCD[k, n] == 1, Min[MultiplicativeOrder[k, n, {-1, 1}]], 0];
a[n_] := Suborder[8, 2 n + 1];
a /@ Range[0, 100] (* Jean-François Alcover, Mar 21 2020, after T. D. Noe in A003558 *)
CROSSREFS
Sequence in context: A259703 A316996 A169589 * A011281 A300731 A100398
KEYWORD
nonn
EXTENSIONS
More terms from Harry J. Smith, Feb 11 2005
Edited by N. J. A. Sloane, May 22 2008 at the suggestion of Jeremy Gardiner
STATUS
approved