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A261514
Indices of Mersenne numbers (A000225) of the form x^2 + xy + y^2.
0
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, 51, 54, 57, 61, 62, 63, 65, 67, 74, 75, 78, 81, 85, 89, 93, 98, 101, 103, 107, 111, 114, 117, 122, 125, 126, 127, 133, 134, 135, 139, 147, 153, 162, 171, 183, 186, 189, 195
OFFSET
1,3
COMMENTS
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.
EXAMPLE
a(4) = 3 because 2^3 - 1 = 1^2 + 1*2 + 2^2 = 7.
a(5) = 5 because 2^5 - 1 = 1^2 + 1*5 + 5^2 = 31.
PROG
(PARI) is(n)=#bnfisintnorm(bnfinit(z^2+z+1), 2^n-1);
for(n=0, 200, if(n==0 || is(n), print1(n, ", ")))
CROSSREFS
Sequence in context: A153763 A345982 A050747 * A215798 A074780 A292938
KEYWORD
nonn
AUTHOR
Altug Alkan, Nov 18 2015
STATUS
approved