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(n-2) and a(n-1) 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
Scott R. Shannon, Table of n, a(n) for n = 1..125.
Wikipedia, Quadratic equation
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
Scott R. Shannon, Nov 17 2022
STATUS
approved