

A283205


Numbers of the form x^2 + y^2 with x and y integers such that x + 3*y is a square.


5



0, 1, 2, 5, 8, 9, 10, 13, 16, 17, 25, 26, 29, 32, 34, 37, 40, 50, 53, 58, 61, 65, 73, 74, 80, 81, 85, 90, 104, 109, 117, 125, 128, 130, 136, 137, 144, 145, 146, 160, 162, 170, 178, 185, 193, 202, 208, 221, 229, 232, 241, 245, 250, 256, 257, 265, 269, 272, 274, 281
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OFFSET

1,3


COMMENTS

This sequence is interesting since part (ii) of the conjecture in A283170 implies that each n = 0,1,2,... can be expressed as the sum of two terms of the current sequence.
Clearly, the sequence is a subsequence of A001481.


LINKS



EXAMPLE

a(1) = 0 since 0 = 0^2 + 0^2 with 0 + 3*0 = 0^2.
a(2) = 1 since 1 = 1^2 + 0^2 with 1 + 3*0 = 1^2.
a(3) = 2 since 2 = 1^2 + 1^2 with 1 + 3*1 = 2^2.
a(4) = 5 since 5 = (2)^2 + 1^2 with (2) + 3*1 = 1^2.
a(5) = 8 since 8 = (2)^2 + 2^2 with (2) + 3*2 = 2^2.
a(6) = 9 since 9 = 0^2 + 3^2 with 0 + 3*3 = 3^2.
a(7) = 10 since 10 = 3^2 + (1)^2 with 3 + 3*(1) = 0^2.


MATHEMATICA

SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]];
n=0; Do[Do[If[SQ[mx^2], Do[If[SQ[(1)^i*x+3(1)^j*Sqrt[mx^2]], n=n+1; Print[n, " ", m]; Goto[aa]], {i, 0, Min[x, 1]}, {j, 0, Min[Sqrt[mx^2], 1]}]], {x, 0, Sqrt[m]}]; Label[aa]; Continue, {m, 0, 281}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



