A270238 Indices of Pell numbers of the form x^2 + xy + y^2.

1, 4, 7, 23, 41, 79, 89, 97, 127, 167, 191, 223, 239, 241, 257, 281, 439, 577, 593

Offset

1,2

Comments

Terms of this sequence are prime numbers most of the time.

Links

Table of n, a(n) for n=1..19.

Example

4 is a term because A000129(4) = 12 and 12 = 2^2 + 2*2 + 2^2.

Prog

(PARI) a000129(n) = ([2, 1; 1, 0]^n)[2, 1];
isA003136(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
for(n=1, 1e3, if(isA003136(a000129(n)), print1(n, ", ")));

Crossrefs

Cf. A000129, A003136.

Sequence in context: A363650 A086968 A101824 * A027946 A348478 A363543

Adjacent sequences: A270235 A270236 A270237 * A270239 A270240 A270241

Keyword

nonn,more

Author

Altug Alkan, Mar 18 2016

Extensions

a(17)-a(19) from Jinyuan Wang, Aug 14 2022

Status

approved