

A056910


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


1



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
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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



