A391050 Greatest prime q such that A391049(n)^2 - 8*q = s^2 for some s > 0.

3, 5, 5, 11, 17, 11, 29, 41, 23, 29, 59, 71, 41, 101, 53, 107, 137, 149, 83, 89, 179, 191, 197, 113, 227, 239, 131, 269, 281, 311, 173, 347, 179, 191, 419, 431, 461, 233, 239, 251, 521, 281, 569, 293, 599, 617, 641, 659, 359, 809, 821, 827, 419, 857, 431, 881, 443

Offset

1,1

Comments

Greatest prime q such that 2*x^2 + A391049(n)*x + q = 0 (equivalently, q*x^2 + A391049(n)*x + 2 = 0) has two rational roots (see second comment in A391049).

For n = 1 and n = 2 there is a second, smaller prime q (2 and 3, respectively) also satisfying the condition; for n > 2 the listed q is unique (see third comment in A391049).

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Formula

If A391049(n) - 2 is prime, then a(n) = A391049(n) - 2, else (A391049(n) - 1)/2.

Example

a(5) = 17 because A391050(5)^2 - 8*17 = 19^2 - 8*17 = 15^2.
a(6) = 11 because A391050(6)^2 - 8*11 = 23^2 - 8*11 = 21^2.

Maple

A391050 := proc(n) if isprime(A391049(n) - 2) then A391049(n) - 2; else 1/2*A391049(n) - 1/2; end if; end proc: seq(A391050(n), n = 1 .. 57);

Crossrefs

Cf. A000040, A067274, A091626, A091627, A364384, A364385, A365876, A365877, A379597, A381710, A381711, A391049.

Sequence in context: A317650 A240731 A266505 * A118132 A089167 A188345

Adjacent sequences: A391047 A391048 A391049 * A391051 A391052 A391053

Keyword

nonn,easy

Author

Felix Huber, Nov 27 2025

Status

approved