

A359048


a(n) is the minimum denominator d such that the decimal expansion of n/d is eventually periodic with periodicity not equal to zero.


0



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

1,1


COMMENTS

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


LINKS



EXAMPLE

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.


MAPLE

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:


PROG

(PARI) a(n) = for(d=1, oo, my(p); if (isprimepower(d, &p) && (10 % p) && (n % d), return(d))); \\ Michel Marcus, Dec 28 2022


CROSSREFS



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EXTENSIONS



STATUS

approved



