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.

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

Offset: 1

Author

Leonardo Sznajder, Dec 14 2022

Keywords

• base
• easy
• hear
• nonn

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

Examples

			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.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Programs

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:
map(f, [$1..100]); # Robert Israel, Jan 19 2023

PARI

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

Extensions

More terms from Michel Marcus, Dec 28 2022