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 1-4 of 4 results.

A060259 Denoting 4 consecutive primes by p, q, r and s, these are the values of q such that q and r have 10 as a primitive root, but p and s do not.

Original entry on oeis.org

59, 109, 179, 229, 571, 701, 937, 1019, 1171, 1429, 1619, 1777, 1811, 1847, 2063, 2269, 2297, 2339, 2383, 2447, 2731, 2819, 2927, 3257, 3299, 3331, 3461, 3571, 3593, 3617, 3701, 3833, 3967, 4139, 4259, 4421, 4567, 4691, 4937, 5087, 5153, 5179, 5417
Offset: 1

Views

Author

Jeff Burch, Mar 23 2001

Keywords

Comments

A prime p has 10 as a primitive root iff the length of the period of the decimal expansion of 1/p is p-1.

Links

Crossrefs

Cf. A001913, A002371, A060260, A060261, A060262.

Programs

  • Mathematica
    test[p_] := MultiplicativeOrder[10, p]===p-1; Prime/@Select[Range[2, 800], test[Prime[ # ]]&&test[Prime[ #+1]]&&!test[Prime[ #-1]]&&!test[Prime[ #+2]]&]
Prime[#+1]&/@SequencePosition[Table[If[MultiplicativeOrder[10,p]===p-1,1,0],{p,Prime[Range[ 800]]}],{0,1,1,0}][[;;,1]] (* Harvey P. Dale, Nov 29 2023 *)

Extensions

Edited by Dean Hickerson, Jun 17 2002
Offset corrected by Amiram Eldar, Oct 03 2021

A060260 Numbers k such that prime(k), prime(k+1) and prime(k+2) have 10 as a primitive root, but prime(k-1) and prime(k+3) do not.

Original entry on oeis.org

55, 75, 141, 164, 184, 199, 358, 371, 380, 432, 559, 702, 745, 808, 825, 858, 882, 1077, 1097, 1279, 1299, 1303, 1328, 1408, 1431, 1486, 1502, 1558, 1654, 1702, 1724, 1744, 1768, 1820, 1835, 1873, 1901, 1905, 1953, 1977, 2050, 2148, 2216, 2220, 2267
Offset: 1

Views

Author

Jeff Burch, Mar 23 2001

Keywords

Comments

A prime p has 10 as a primitive root iff the length of the period of the decimal expansion of 1/p is p-1.

Links

Crossrefs

The corresponding primes are in A060261.
Cf. A001913, A002371, A060259, A060262.

Programs

  • Mathematica
    test[p_] := MultiplicativeOrder[10, p]===p-1; Select[Range[2, 2500], test[Prime[ # ]]&&test[Prime[ #+1]]&&test[Prime[ #+2]]&&!test[Prime[ #-1]]&&!test[Prime[ #+3]]&]

Extensions

Edited by Dean Hickerson, Jun 17 2002

A060261 Denoting 5 consecutive primes by p, q, r, s and t, these are the values of q such that q, r and s have 10 as a primitive root, but p and t do not.

Original entry on oeis.org

257, 379, 811, 971, 1097, 1217, 2411, 2539, 2617, 3011, 4051, 5297, 5657, 6211, 6337, 6659, 6857, 8647, 8807, 10457, 10651, 10687, 10937, 11731, 11939, 12451, 12577, 13099, 14011, 14537, 14731, 14887, 15137, 15607, 15737, 16091, 16411
Offset: 1

Views

Author

Jeff Burch, Mar 23 2001

Keywords

Comments

A prime p has 10 as a primitive root iff the length of the period of the decimal expansion of 1/p is p-1.

Links

Crossrefs

The indices of these primes are in A060260.
Cf. A001913, A002371, A060259, A060262.

Programs

  • Mathematica
    test[p_] := MultiplicativeOrder[10, p]===p-1; Prime/@Select[Range[2, 2500], test[Prime[ # ]]&&test[Prime[ #+1]]&&test[Prime[ #+2]]&&!test[Prime[ #-1]]&&!test[Prime[ #+3]]&]

Extensions

Edited by Dean Hickerson, Jun 17 2002
Offset corrected by Amiram Eldar, Oct 03 2021

A060263 a(n) = smallest prime q such that precisely n successive primes p starting at q have reciprocals with period p-1 and prevprime(q) is not such a prime.

Original entry on oeis.org

59, 257, 17, 487, 5737, 23459, 364379, 681899, 4275343, 14747137, 12284017, 61598897, 62232899, 95386019, 824443051, 2245849783
Offset: 2

Views

Author

Jeff Burch, Mar 23 2001

Keywords

Crossrefs

Cf. A002371, A048595, A060262.

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 21 2003
a(6) onward corrected and title clarified by Sean A. Irvine, Nov 05 2022
Showing 1-4 of 4 results.

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

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