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%I #17 Nov 25 2015 02:24:07
%S 0,1,2,3,5,6,7,9,13,14,15,17,18,19,21,25,26,27,31,37,38,39,42,45,49,
%T 51,54,57,61,62,63,65,67,74,75,78,81,85,89,93,98,101,103,107,111,114,
%U 117,122,125,126,127,133,134,135,139,147,153,162,171,183,186,189,195
%N Indices of Mersenne numbers (A000225) of the form x^2 + xy + y^2.
%C Inspired by intersection of nice and core sequences. Initial Mersenne numbers of the form x^2 + xy + y^2 are 0, 1, 3, 7, 31, 63, 127, 511, 8191, 16383.
%e a(4) = 3 because 2^3 - 1 = 1^2 + 1*2 + 2^2 = 7.
%e a(5) = 5 because 2^5 - 1 = 1^2 + 1*5 + 5^2 = 31.
%o (PARI) is(n)=#bnfisintnorm(bnfinit(z^2+z+1), 2^n-1);
%o for(n=0, 200, if(n==0 || is(n), print1(n, ", ")))
%Y Cf. A000225, A003136.
%K nonn
%O 1,3
%A _Altug Alkan_, Nov 18 2015