A261514 Indices of Mersenne numbers (A000225) of the form x^2 + xy + y^2.

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.

Links

Table of n, a(n) for n=1..63.

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

Cf. A000225, A003136.

Sequence in context: A153763 A345982 A050747 * A215798 A074780 A292938

Adjacent sequences: A261511 A261512 A261513 * A261515 A261516 A261517

Keyword

nonn

Author

Altug Alkan, Nov 18 2015

Status

approved