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A070683
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Smallest m in range 1..phi(2n+1) such that 12^m == 1 mod 2n+1, or 0 if no such number exists.
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11
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0, 0, 4, 6, 0, 1, 2, 0, 16, 6, 0, 11, 20, 0, 4, 30, 0, 12, 9, 0, 40, 42, 0, 23, 42, 0, 52, 4, 0, 29, 15, 0, 4, 66, 0, 35, 36, 0, 6, 26, 0, 41, 16, 0, 8, 6, 0, 12, 16, 0, 100, 102, 0, 53, 54, 0, 112, 44, 0, 48, 11, 0, 100, 126, 0, 65, 6, 0, 136, 138, 0, 2, 4, 0, 148
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OFFSET
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0,3
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COMMENTS
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LINKS
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MAPLE
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f:= proc(n)
if n mod 3 = 1 then 0 else numtheory:-order(12, 2*n+1) fi
end proc:
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MATHEMATICA
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a[n_] := Module[{s}, s = SelectFirst[Range[EulerPhi[2n+1]], PowerMod[12, #, 2n+1] == 1&]; If[s === Missing["NotFound"], 0, s]];
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CROSSREFS
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Cf. A070667-A070675, A002326, A019340, A070676, A053447, A070677, A070678, A053451, A070679, A070682, A070680, A070681.
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KEYWORD
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AUTHOR
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STATUS
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approved
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