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.

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

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

A060262 a(n) is the smallest k such that prime(k), prime(k+1), ..., prime(k+n-1) all have 10 as a primitive root, but prime(k-1) and prime(k+n) do not.

Original entry on oeis.org

4, 17, 55, 7, 93, 754, 2611, 31092, 55207, 301252, 955428, 805428, 3651249, 3686621, 5510710, 42337888, 109670084, 590903433, 1010572448
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.
a(21) = 9774718453 and a(23) = 9525468065. - Amiram Eldar, Oct 03 2021

Crossrefs

Cf. A001913, A002371, A060259, A060260, A060261.

Programs

  • Mathematica
    test[p_] := MultiplicativeOrder[10, p]===p-1; For[n=1, n<100, n++, a[n]=0]; v=4; While[True, For[n=1, test[Prime[v+n]], n++, Null]; If[a[n]==0, a[n]=v; Print["a(", n, ") = ", v]]; For[v+=n+1, !test[Prime[v]], v++, Null]]

Extensions

Edited by Dean Hickerson, Jun 17 2002
a(13)-a(19) from Amiram Eldar, Oct 03 2021
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.