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(n-2)*x^2 + a(n-1)*x + a(n) = 0 has at least one integer root.
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
Offset: 1
Keywords
Examples
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.
Links
- Scott R. Shannon, Table of n, a(n) for n = 1..125.
- Wikipedia, Quadratic equation
Comments