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.

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

Author

Jeff Burch, Mar 23 2001

Keywords

• nonn

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

• Amiram Eldar, Table of n, a(n) for n = 1..10000

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