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.

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

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 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