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.

A129727 Primes p for which the period length of 1/p is a semiprime.

Original entry on oeis.org

7, 13, 23, 31, 43, 47, 59, 67, 71, 101, 103, 139, 167, 179, 191, 263, 277, 283, 293, 311, 383, 431, 439, 443, 503, 547, 557, 599, 607, 613, 653, 683, 787, 809, 827, 853, 859, 863, 887, 947, 983, 997, 1013, 1019, 1039, 1163, 1213, 1237, 1321, 1367, 1399, 1423
Offset: 1

Views

Author

Jonathan Vos Post, May 12 2007

Keywords

Comments

The prime index of A122183. Semiprime analog of A072859 = primes p for which the period length of 1/p is prime. Based upon A002371 = period of decimal expansion of 1/(n-th prime).

Examples

			a(1) = 7 because A000040(4) Period of decimal expansion of 1/7 = 6 = 2*3, a semiprime.
a(2) = 13 because A000040(6) = 6 = 2*3.
a(3) = 23 because A000040(9) = 22 = 2*11.
a(4) = 31 because A000040(11) = 15 = 3*5.
a(5) = 43 because A000040(14) = 21 = 3*7.
a(6) = 47 because A000040(15) = 46 = 2*23.
a(7) = 59 because A000040(17) = 58 = 2*29.

Links

Crossrefs

Cf. A000040, A001358, A002371, A072859, A128948.

Programs

  • Mathematica
    fQ[p_] := Plus @@ Last /@ FactorInteger@Length@RealDigits[1/p][[1, 1]] == 2;; lst = {}; Do[ p = Prime@n; If[ fQ@p, AppendTo[lst, p]], {n, 230}] (* Robert G. Wilson v *)

A197225 Primes p with the period of the decimal fraction 1/p a prime power, A000961.

Original entry on oeis.org

3, 11, 17, 37, 41, 53, 73, 79, 83, 101, 107, 137, 163, 173, 227, 239, 257, 271, 317, 347, 353, 359, 449, 467, 479, 563, 587, 641, 643, 719, 733, 751, 757, 773, 797, 839, 907, 1031, 1187, 1231, 1283, 1307, 1319, 1409, 1439, 1493, 1523, 1627, 1637, 1879, 1907
Offset: 1

Views

Author

T. D. Noe, Oct 22 2011

Keywords

Links

Crossrefs

Cf. A072859 (period is prime).
Cf. A072982 (period is a power of 2).
Cf. A128948 (period is perfect power).
Cf. A197226 (the periods of this sequence).
Cf. A129727 (period is a semiprime).

Programs

  • Mathematica
    myPerfectPowerQ[n_] := Length[FactorInteger[n]] == 1; Select[Prime[Range[500]], Mod[10,#] > 0 && myPerfectPowerQ[Length[RealDigits[1/#, 10][[1,1]]]] &]

A122183 Primes p_i by index i for which the period length of 1/p_i is a semiprime.

Original entry on oeis.org

4, 6, 9, 11, 14, 15, 17, 19, 20, 26, 27, 34, 39, 41, 43, 56, 59, 61, 62, 64, 76, 83, 85, 86, 96, 101, 102, 109, 111, 112, 119, 124, 138, 140, 144, 147, 149, 150, 154, 161, 166, 168, 170, 171, 175, 192, 198, 203, 216, 219, 222, 224, 225, 235, 236, 239, 240, 246, 251
Offset: 1

Views

Author

Jonathan Vos Post, May 10 2007

Keywords

Comments

Semiprime analog of A072859 based on A002371.
Numbers n such that A002371(n) is an element of A001358.

Examples

			a(1) = 4 because A002371(4) Period of decimal expansion of 1/(4th prime) = 6 = 2*3, a semiprime.
a(2) = 6 because A002371(6) = 6 = 2*3.
a(3) = 9 because A002371(9) = 22 = 2*11.
a(4) = 11 because A002371(11) = 15 = 3*5.
a(5) = 14 because A002371(14) = 21 = 3*7.
a(6) = 15 because A002371(15) = 46 = 2*23.
a(7) = 17 because A002371(17) = 58 = 2*29.

Crossrefs

Cf. A000040, A001358, A002371, A072859, A128948.

Programs

  • Mathematica
    semiprimeQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; PrimePi /@ Select[Prime@ Range@ 254, semiprimeQ@ MultiplicativeOrder[10, # ] &] (* Robert G. Wilson v *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, May 22 2007
Showing 1-3 of 3 results.

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

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