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A056910 Numbers n where 36n^2+12n+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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

36m^2+12m+7=(6m+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

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)