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A333339
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a(n) is the smallest positive number k such that n divides 3^k - k.
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4
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1, 1, 3, 3, 7, 3, 2, 3, 9, 7, 4, 3, 16, 5, 27, 11, 5, 9, 29, 7, 27, 45, 39, 3, 73, 27, 27, 27, 22, 27, 132, 27, 36, 5, 27, 27, 65, 29, 27, 27, 27, 27, 10, 59, 27, 39, 12, 27, 47, 73, 42, 27, 68, 27, 36, 27, 30, 47, 154, 27, 192, 147, 27, 59, 16, 45, 119, 75, 39
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OFFSET
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1,3
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COMMENTS
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For any positive integer n, if k = a(n) + n*m*A007734(n) and m >= 0 then 3^k - k is divisible by n.
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LINKS
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FORMULA
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a(3^m) = 3^m for m >= 0.
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MAPLE
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f:= proc(n) local k;
for k from 1 do if 3 &^k - k mod n = 0 then return k fi od
end proc:
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MATHEMATICA
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a[n_] := Module[{k = 1}, While[!Divisible[3^k - k, n], k++]; k]; Array[a, 100] (* Amiram Eldar, Mar 16 2020 *)
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PROG
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(PARI) a(n) = for(k=1, oo, if(Mod(3, n)^k==k, return(k)));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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