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A056910 Numbers k such that 36*k^2 + 12*k + 7 is prime (sorted by absolute values with negatives before positives). 1

%I

%S 0,-1,-2,3,4,5,-6,10,-11,13,-15,15,18,-22,24,25,29,-31,33,-37,-45,-55,

%T 55,59,-67,-72,74,80,-81,85,-86,88,-90,-95,99,-101,-102,108,-116,118,

%U -122,129,-130,143,148,-151,-155,-157,158,159,-162,164,165

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

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

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

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

%Y 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.

%K sign

%O 0,3

%A _Henry Bottomley_, Jul 07 2000

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Last modified July 13 03:03 EDT 2020. Contains 335673 sequences. (Running on oeis4.)