A056910 Numbers k such that 36*k^2 + 12*k + 7 is prime (sorted by absolute values with negatives before positives).

0, -1, -2, 3, 4, 5, -6, 10, -11, 13, -15, 15, 18, -22, 24, 25, 29, -31, 33, -37, -45, -55, 55, 59, -67, -72, 74, 80, -81, 85, -86, 88, -90, -95, 99, -101, -102, 108, -116, 118, -122, 129, -130, 143, 148, -151, -155, -157, 158, 159, -162, 164, 165

Offset

0,3

Comments

36*k^2 + 12*k + 7 = (6*k+1)^2 + 6, which is six more than a square.

Links

Table of n, a(n) for n=0..52.

Formula

a(n) = (-1 +- sqrt(A056909(n) - 6))/6, choosing +- to give an integer result for each n.

Example

a(2)=-2 since 36*(-2)^2 + 12*(-2) + 7 = 127, which is prime (as well as being six more than a square).

Crossrefs

This sequence and formula generate all primes of the form k^2+6, i.e., A056909. Except for the first term, none of the a(n) are a multiple of 7 and so the rest of this sequence is a subsequence of A047304. Cf. A056900, A056902, A056904, A056906, A056907, A056908.

Sequence in context: A023761 A032902 A018578 * A212774 A131934 A066501

Adjacent sequences: A056907 A056908 A056909 * A056911 A056912 A056913

Keyword

sign

Author

Henry Bottomley, Jul 07 2000

Status

approved