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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.

%I A060259 #13 Nov 29 2023 19:18:50
%S A060259 59,109,179,229,571,701,937,1019,1171,1429,1619,1777,1811,1847,2063,
%T A060259 2269,2297,2339,2383,2447,2731,2819,2927,3257,3299,3331,3461,3571,
%U A060259 3593,3617,3701,3833,3967,4139,4259,4421,4567,4691,4937,5087,5153,5179,5417
%N 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.
%C A060259 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.
%H A060259 Amiram Eldar, <a href="/A060259/b060259.txt">Table of n, a(n) for n = 1..10000</a>
%t A060259 test[p_] := MultiplicativeOrder[10, p]===p-1; Prime/@Select[Range[2, 800], test[Prime[ # ]]&&test[Prime[ #+1]]&&!test[Prime[ #-1]]&&!test[Prime[ #+2]]&]
%t A060259 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 *)
%Y A060259 Cf. A001913, A002371, A060260, A060261, A060262.
%K A060259 nonn
%O A060259 1,1
%A A060259 _Jeff Burch_, Mar 23 2001
%E A060259 Edited by _Dean Hickerson_, Jun 17 2002
%E A060259 Offset corrected by _Amiram Eldar_, Oct 03 2021