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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.

%I A359048 #35 Jan 18 2025 09:07:11
%S A359048 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,
%T A359048 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,
%U A359048 7,3,3,7,3,3,7,3,3,7,3,3,7,3,3,9,3,3,7,3,3,7
%N 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.
%C A359048 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
%H A359048 Antti Karttunen, <a href="/A359048/b359048.txt">Table of n, a(n) for n = 1..20000</a>
%e A359048 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.
%p A359048 f:= proc(n) local d;
%p A359048 for d from 3 by 2 do
%p A359048   if (n mod d <> 0) and (d mod 5 <> 0) and nops(numtheory:-factorset(d))=1 then return d fi
%p A359048 od
%p A359048 end proc:
%p A359048 map(f, [$1..100]); # _Robert Israel_, Jan 19 2023
%o A359048 (PARI) a(n) = for(d=1, oo, my(p); if (isprimepower(d, &p) && (10 % p) && (n % d), return(d))); \\ _Michel Marcus_, Dec 28 2022
%K A359048 base,easy,hear,nonn
%O A359048 1,1
%A A359048 _Leonardo Sznajder_, Dec 14 2022
%E A359048 More terms from _Michel Marcus_, Dec 28 2022