%I #30 Feb 17 2023 20:18:21

%S 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 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 7,3,3,7,3,3,7,3,3,7,3,3,7,3,3,9,3,3,7,3,3,7

%N 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 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

%e 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 f:= proc(n) local d;

%p for d from 3 by 2 do

%p if (n mod d <> 0) and (d mod 5 <> 0) and nops(numtheory:-factorset(d))=1 then return d fi

%p od

%p end proc:

%p map(f, [$1..100]); # _Robert Israel_, Jan 19 2023

%o (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 base,easy,hear,nonn

%O 1,1

%A _Leonardo Sznajder_, Dec 14 2022

%E More terms from _Michel Marcus_, Dec 28 2022