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A273614 Numbers k such that 3k - 1 divides 3^k - 1.

%I A273614 #33 Jun 29 2024 16:43:52
%S A273614 1,9,12,96,345,432,852,945,1452,2160,3480,3753,4800,6561,6984,13230,
%T A273614 15840,17040,30210,31008,40320,43776,44352,44652,47628,55200,56940,
%U A273614 60420,61065,69312,71145,74100,77400,81504,125580,128016,175952,192240,198168
%N A273614 Numbers k such that 3k - 1 divides 3^k - 1.
%H A273614 Charles R Greathouse IV, <a href="/A273614/b273614.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Alois P. Heinz)
%p A273614 a:= proc(n) option remember; local k;
%p A273614       if n=1 then 1 else for k from 1+a(n-1)
%p A273614       while 3&^k mod(3*k-1)<>1 do od; k fi
%p A273614     end:
%p A273614 seq(a(n), n=1..40);  # _Alois P. Heinz_, May 27 2016
%t A273614 Select[Range[10^6], PowerMod[3, #, 3*# - 1] == 1 &] (* _Giovanni Resta_, May 27 2016 *)
%o A273614 (Magma)  [n: n in [1..200000] | Modexp(3, n, 3*n-1) eq 1];
%o A273614 (PARI) is(n)=Mod(3,3*n-1)^n==1 \\ _Charles R Greathouse IV_, May 29 2016
%Y A273614 Cf. A024023, A081856, A233415.
%K A273614 nonn
%O A273614 1,2
%A A273614 _Juri-Stepan Gerasimov_, May 26 2016