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

1,1

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

Table of n, a(n) for n=1..90.

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

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

Sequence in context: A366982 A366973 A076560 * A096915 A249806 A249382

Adjacent sequences: A359045 A359046 A359047 * A359049 A359050 A359051

Keyword

base,easy,hear,nonn

Author

Leonardo Sznajder, Dec 14 2022

Extensions

More terms from Michel Marcus, Dec 28 2022

Status

approved