

A358462


a(1) = 1, a(2) = 1; for n > 2, a(n) is smallest magnitude nonzero integer which has not appeared such that the quadratic equation a(n2)*x^2 + a(n1)*x + a(n) = 0 has at least one integer root.


1



1, 1, 2, 3, 2, 5, 3, 8, 4, 12, 8, 4, 12, 16, 28, 44, 24, 20, 44, 24, 20, 56, 32, 88, 48, 40, 112, 64, 176, 48, 128, 64, 192, 256, 256, 512, 768, 512, 1280, 768, 2048, 1024, 3072, 2048, 1024, 3072, 4096, 7168, 11264, 6144, 5120, 11264, 6144, 5120, 14336, 8192
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OFFSET

1,3


COMMENTS

As a(8) and a(9) are both even, all subsequent terms will be even. This is due to the discriminant having to equal a square, and with both a(n2) and a(n1) being even, a(n) must also be even.
Although only one root must be an integer, several terms result in two integers as roots. For example a(3) = 2, a(4) = 3, a(11) = 8, a(14) = 16, a(34) = 256 all produce two integer roots.


LINKS



EXAMPLE

a(3) = 2 as a(1)*x^2 + a(2)*x + a(3) = x^2  x  2 which has the integer roots x = 1 and x = 2, and 2 has not previously appeared.
a(6) = 5 as a(4)*x^2 + a(5)*x + a(6) = 3*x^2 + 2*x  5 which has the integer root x = 1, and 5 has not previously appeared.


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



