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A070191 Numbers k such that gcd(3*k, 8^k+1) = 3. 4

%I #20 Jun 14 2022 02:26:11

%S 1,5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,59,61,65,67,71,73,

%T 77,79,83,85,89,91,95,97,101,103,107,109,113,115,119,121,125,127,131,

%U 133,137,139,143,145,149,151,155,157,161,163,167,169,173,175,179,181

%N Numbers k such that gcd(3*k, 8^k+1) = 3.

%C The listed terms are the same as those in A069040, but the sequences are not identical. (The similarity is mostly explained by the absence of multiples of 2, 3 and 55 from both sequences.) See A070192 and A070193 for the differences.

%C The number of terms not exceeding 10^m, for m = 1, 2, ..., are 3, 32, 325, 3244, 32468, 324667, 3246642, 32466291, 324662816, 3246627133, ... . Apparently, the asymptotic density of this sequence exists and equals 0.32466... . - _Amiram Eldar_, Jun 14 2022

%H Seiichi Manyama, <a href="/A070191/b070191.txt">Table of n, a(n) for n = 1..10000</a>

%t test8[n_] := GCD[3n, PowerMod[8, n, 3n]+1]==3; Select[Range[200], test8]

%Y Cf. A069254.

%Y Cf. A069040, A070192, A070193.

%K nonn

%O 1,2

%A _Benoit Cloitre_ and _Dean Hickerson_, Apr 26 2002

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