A087002 -id:A087002 - cp's OEIS frontend

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

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

Reinhard Zumkeller, Jul 29 2003

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

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

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

Reinhard Zumkeller, Jul 29 2003

a(n) = floor(A086999(n)/10^A087000(n)); A055642(a(n))=A087000(n);

a(n) + A087002(n) = 10^A087000(n) - 1.

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

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

Eric Weisstein's World of Mathematics, Midy's Theorem
Index entries for sequences related to decimal expansion of 1/n.

A086999 Periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

Original entry on oeis.org

142857, 90, 769230, 5882352941176470, 526315789473684210, 4347826086956521739130, 3448275862068965517241379310, 2127659574468085106382978723404255319148936170

Offset: 1

Reinhard Zumkeller, Jul 29 2003

A087001(n)=floor(a(n)/10^A087000(n)), A087002(n)=a(n) mod 10^A087000(n);
A087001(n) + A087002(n) = 10^A087000(n) - 1;
a(n) = A087001(n)*10^A087000(n) + A087002(n).

			p=73: a(11)=A060283(21)=13698630 -> [1369][8630] ->
A087001(11)=1369, A087002(11)=8630, A087001(11)+A087002(11)=1369+8630=9999.

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

Eric Weisstein's World of Mathematics, Decimal Expansion
Eric Weisstein's World of Mathematics, Repeating Decimal
Eric Weisstein's World of Mathematics, Midy's Theorem
Index entries for sequences related to decimal expansion of 1/n.

a(n)=A060283(A049084(A0A028416(n))), A002283.

cp's OEIS Frontend

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

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

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A086999 Periodic part of decimal expansion of 1/p for those primes having a periodic part of even length.

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