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 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 (list; graph; refs; listen; history; text; internal format)
 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 half-reduced 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 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

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Last modified July 25 12:56 EDT 2021. Contains 346290 sequences. (Running on oeis4.)