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A334487
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a(n) = p(n, 2)*p(n, 5)/p(n, 10) where p(n, b) is the period of repeating digits of 1/n in base b.
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2
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1, 1, 4, 1, 4, 4, 3, 2, 36, 4, 25, 4, 8, 3, 8, 4, 8, 36, 9, 4, 6, 25, 11, 4, 20, 8, 108, 3, 14, 8, 1, 8, 50, 8, 12, 36, 432, 9, 8, 8, 80, 6, 28, 25, 72, 11, 23, 8, 21, 20, 8, 8, 208, 108, 50, 3, 18, 14, 29, 8, 30, 1, 6, 16, 8, 50, 44, 8, 22, 12, 5, 36, 81, 432, 40
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OFFSET
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1,3
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LINKS
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FORMULA
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MATHEMATICA
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f[n_, p_] := MultiplicativeOrder[p, n/(p^IntegerExponent[n, p])]; a[n_] := f[n, 2] * f[n, 5] / MultiplicativeOrder[10, n / 2^IntegerExponent[n, 2] / 5^IntegerExponent[n, 5]]; Array[a, 100] (* Amiram Eldar, May 04 2020 *)
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PROG
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(PARI)
a2(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ A007733
a5(n) = znorder(Mod(5, n/5^valuation(n, 5))); \\ A007736
a10(n) = znorder(Mod(10, n/2^valuation(n, 2)/5^valuation(n, 5))); \\ A007732
a(n) = a2(n)*a5(n)/a10(n);
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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