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A216469 a(n) = smallest m such that 2n-1 | (2^m+1)/3, or 0 if no such m exists.

%I A216469 #51 Jul 09 2025 04:34:54
%S A216469 1,3,0,0,9,5,0,0,0,9,0,0,0,27,0,0,15,0,0,0,0,7,0,0,0,0,0,0,9,29,0,0,0,
%T A216469 33,0,0,0,0,0,0,81,41,0,0,0,0,0,0,0,45,0,0,0,53,0,0,0,0,0,0,55,0,0,0,
%U A216469 21,65,0,0,0,69,0,0,0,0,0,0,0,0,0,0,0,81,0,0
%N A216469 a(n) = smallest m such that 2n-1 | (2^m+1)/3, or 0 if no such m exists.
%t A216469 Table[s = MultiplicativeOrder[2, 3*(2*n-1), {-1}]; If[IntegerQ[s], s, 0], {n, 100}] (* _T. D. Noe_, Sep 11 2012 *)
%o A216469 (PARI) for(i=0,200,i++;m=0;for(x=0,i,x++;if(((2^x+1)/3)%i==0,m=x;break));print1(m",")) \\ _V. Raman_, Nov 22 2012
%Y A216469 Cf. A003558, A002326, A216829, A216833.
%Y A216469 Cf. A216833 (multiplicative order of 2 mod 3*(2n-1)).
%Y A216469 Cf. A216829 (value of the half of the multiplicative order of 2 mod 3*(2n-1)).
%K A216469 nonn
%O A216469 1,2
%A A216469 _V. Raman_, Sep 07 2012