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A359048
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a(n) is the minimum denominator d such that the decimal expansion of n/d is eventually periodic with periodicity not equal to zero.
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0
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3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 9, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 9, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 11, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 7, 3, 3, 9, 3, 3, 7, 3, 3, 7
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OFFSET
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1,1
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COMMENTS
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a(n) is the smallest prime power p^e that does not divide n, where p is a prime that doesn't divide 10, and e >= 1. - Jon E. Schoenfield, Dec 24 2022
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LINKS
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EXAMPLE
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For n=21, a(21) = 9 because 21/9 = 2.333... (periodic) and 9 is the first number with that property for numerator 21. That's because 21/2 = 10.5, 21/3 = 7, 21/4 = 5.25, 21/5 = 4.2, 21/6 = 3.5, 21/7 = 3 and 21/8 = 2.625.
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MAPLE
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f:= proc(n) local d;
for d from 3 by 2 do
if (n mod d <> 0) and (d mod 5 <> 0) and nops(numtheory:-factorset(d))=1 then return d fi
od
end proc:
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PROG
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(PARI) a(n) = for(d=1, oo, my(p); if (isprimepower(d, &p) && (10 % p) && (n % d), return(d))); \\ Michel Marcus, Dec 28 2022
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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