A334487 a(n) = p(n, 2)*p(n, 5)/p(n, 10) where p(n, b) is the period of repeating digits of 1/n in base b.

1, 1, 4, 1, 4, 4, 3, 2, 36, 4, 25, 4, 8, 3, 8, 4, 8, 36, 9, 4, 6, 25, 11, 4, 20, 8, 108, 3, 14, 8, 1, 8, 50, 8, 12, 36, 432, 9, 8, 8, 80, 6, 28, 25, 72, 11, 23, 8, 21, 20, 8, 8, 208, 108, 50, 3, 18, 14, 29, 8, 30, 1, 6, 16, 8, 50, 44, 8, 22, 12, 5, 36, 81, 432, 40

Offset

1,3

Links

Michel Marcus, Table of n, a(n) for n = 1..5000

Formula

a(n) = A007733(n)*A007736(n)/A007732(n).

Mathematica

f[n_, p_] := MultiplicativeOrder[p, n/(p^IntegerExponent[n, p])]; a[n_] := f[n, 2] * f[n, 5] / MultiplicativeOrder[10, n / 2^IntegerExponent[n, 2] / 5^IntegerExponent[n, 5]]; Array[a, 100] (* Amiram Eldar, May 04 2020 *)

Prog

(PARI)
a2(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ A007733
a5(n) = znorder(Mod(5, n/5^valuation(n, 5))); \\ A007736
a10(n) = znorder(Mod(10, n/2^valuation(n, 2)/5^valuation(n, 5))); \\ A007732
a(n) = a2(n)*a5(n)/a10(n);

Crossrefs

Cf. A007733, A007736, A007732, A334488.

Sequence in context: A321593 A173259 A021711 * A327304 A117445 A145079

Adjacent sequences: A334484 A334485 A334486 * A334488 A334489 A334490

Keyword

nonn,base

Author

Michel Marcus, May 03 2020

Status

approved