cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A087000 Half length of periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

Original entry on oeis.org

3, 1, 3, 8, 9, 11, 14, 23, 29, 30, 4, 22, 48, 2, 17, 54, 56, 21, 65, 4, 23, 74, 39, 83, 89, 90, 96, 49, 15, 111, 114, 116, 15, 25, 128, 131, 134, 14, 73, 156, 55, 168, 58, 16, 183, 93, 189, 191, 194, 100, 102, 209, 70, 216, 16, 76, 230, 77, 243, 245, 249, 251
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 29 2003

Keywords

Comments

a(n) appears to be the least k such that 10^k+1 is divisible by A028416(n). See A001271. - Michel Marcus, Aug 13 2023

Links

Crossrefs

Cf. A028416, A002371, A086999, A087001, A087002, A001271, A062397 (10^n+1).

Formula

a(n) = A002371(A049084(A028416(n)))/2.
a(n) = A055642(A086999(n))/2.
a(n) = A055642(A087001(n)) = A055642(A087002(n)).

A087001 Left half of periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

Original entry on oeis.org

142, 9, 769, 58823529, 526315789, 43478260869, 34482758620689, 21276595744680851063829, 16949152542372881355932203389, 163934426229508196721311475409, 1369, 1123595505617977528089
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 29 2003

Keywords

Comments

a(n) = floor(A086999(n)/10^A087000(n)); A055642(a(n))=A087000(n);
a(n) + A087002(n) = 10^A087000(n) - 1.

Examples

			p=17: A086999(4)=5882352941176470 -> [58823529][41176470] ->
A087001(4)=58823529, A087002(4)=41176470,
A087001(4)+A087002(4)=58823529+41176470=99999999.

References

  • H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, Die periodischen Dezimalbrueche.

Links

A087002 Right half of periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

Original entry on oeis.org

857, 0, 230, 41176470, 473684210, 56521739130, 65517241379310, 78723404255319148936170, 83050847457627118644067796610, 836065573770491803278688524590, 8630, 8876404494382022471910
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 29 2003

Keywords

Comments

a(n) = A086999(n) mod 10^A087000(n); A055642(a(n))=A087000(n);
A087001(n) + a(n) = 10^A087000(n) - 1.

Examples

			p=19: A086999(5)=526315789473684210 -> [526315789][473684210] ->
A087001(5)=526315789, A087002(5)=473684210,
A087001(5)+A087002(5)=526315789+473684210=999999999.

References

  • H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, Die periodischen Dezimalbrueche.

Links

Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.