

A344232


All positive integers k represented properly by the positive definite binary quadratic for 2*X^2 + 2*X*Y + 3*Y^2 = k, ordered increasingly.


4



2, 3, 7, 10, 15, 18, 23, 27, 35, 42, 43, 47, 58, 63, 67, 82, 83, 87, 90, 98, 103, 107, 115, 122, 123, 127, 135, 138, 147, 162, 163, 167, 178, 183, 202, 203, 207, 210, 215, 218, 223, 227, 235, 243, 258, 263, 267, 282, 283, 287, 290, 298, 303, 307, 315, 322, 327, 335, 343, 347, 362, 367, 378, 383, 387
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OFFSET

1,1


COMMENTS

This is one of the sequences bisecting A343238, The other sequence is given in A344231.
The primes of this sequence are given in A106865.
See A344231 for references and links on parallel forms and halfreduced right neighbor forms (R(t)transformations), and also for the remark on the equivalent reduced form [2, 2, 3].
The form [2, 2, 3] given in the name is one of the two inequivalent reduced primitive forms of discriminant Disc = 20.
The neighboring numbers k (twins) begin: [42, 43], [82, 83], [122, 123] [162, 163], [202, 203], [282, 283], ...
For the solutions (X, Y) of F2 = [2, 2, 3] representing k = a(n) see A344234.


LINKS

Table of n, a(n) for n=1..65.


FORMULA

For the a(n) definition see the name: 2*X^2 + 2*X*Y + 3*Y^2 = a(n) has proper solutions, and only for these values.


CROSSREFS

Cf. A106865, A343238, A343239, A343240, A344231, A344234.
Sequence in context: A002255 A272649 A266813 * A192116 A088163 A048448
Adjacent sequences: A344229 A344230 A344231 * A344233 A344234 A344235


KEYWORD

nonn,easy


AUTHOR

Wolfdieter Lang, May 19 2021


STATUS

approved



