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.

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

1,1

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, 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 *)

Crossrefs

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

Sequence in context: A142298 A231978 A180947 * A141934 A044246 A044627

Adjacent sequences: A060256 A060257 A060258 * A060260 A060261 A060262

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