A007736 -id:A007736 - cp's OEIS frontend

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

Michel Marcus, May 03 2020

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

Cf. A007733, A007736, A007732, A334488.

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 *)

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);

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

A334488 Numbers m for which p(m, 2)*p(m, 5) = p(m, 10), where p(m, b) is the period of repeating digits of 1/m in base b.

Original entry on oeis.org

1, 2, 4, 31, 62, 124, 601, 1202, 2404, 2593, 4808, 5186, 9616, 10372, 18631, 20744, 37262, 41488, 74524, 82976, 149048, 165952, 298096, 331904, 599479, 1198958, 2397916, 204700049, 409400098, 466344409, 668731841, 818800196, 932688818, 1023500245, 1337463682, 1554449047

Offset: 1

Michel Marcus, May 03 2020

Numbers m such that A334487(m) = 1.

Ray Chandler, Table of n, a(n) for n = 1..56 (first 45 terms from Giovanni Resta)
Robert G. Wilson v and Ray Chandler, Known terms (not exhaustive)

Cf. A007733, A007736, A007732, A334487.

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
isok(m) = a2(m)*a5(m) == a10(m);

a(28) from Jinyuan Wang, May 03 2020

a(29)-a(36) from Giovanni Resta, May 04 2020

cp's OEIS Frontend

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.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula