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