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

1,1

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

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]]&]
pr10Q[{a_, b_, c_, d_, e_}]:=Boole[PrimitiveRoot[#, 10]==10&/@{a, b, c, d, e}]=={0, 1, 1, 1, 0}; Select[Partition[Prime[Range[5000]], 5, 1], pr10Q][[;; , 2]] (* Harvey P. Dale, Oct 18 2025 *)

Crossrefs

The indices of these primes are in A060260.

Cf. A001913, A002371, A060259, A060262.

Sequence in context: A256776 A252279 A105345 * A264348 A301619 A340343

Adjacent sequences: A060258 A060259 A060260 * A060262 A060263 A060264

Keyword

nonn

Author

Jeff Burch, Mar 23 2001

Extensions

Edited by Dean Hickerson, Jun 17 2002

Offset corrected by Amiram Eldar, Oct 03 2021

Status

approved