

A237037


Numbers k such that (2*k)^3 + 1 is a semiprime.


8



1, 2, 3, 8, 9, 11, 14, 21, 29, 30, 35, 36, 39, 50, 51, 53, 56, 74, 78, 81, 95, 105, 116, 140, 155, 165, 176, 179, 191, 198, 224, 228, 245, 284, 303, 336, 378, 393, 410, 413, 414, 428, 429, 438, 464, 485, 491, 504, 506, 515, 534, 546, 554, 575, 596, 611, 638, 641, 648, 659, 680, 683, 711, 714, 725, 744, 765, 774, 791
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OFFSET

1,2


COMMENTS

Numbers k such that 2*k+1 and 4*k^2  2*k + 1 are both prime.
Same as k/2 such that k^3 + 1 is a semiprime, because then k must be even.


LINKS

Eric Weisstein's World of Mathematics, Semiprime.


FORMULA



EXAMPLE

(2*1)^3 + 1 = 9 = 3*3 is a semiprime, so a(1) = 1.


MATHEMATICA

Select[Range[800], PrimeQ[(2 #)^2  2 # + 1] && PrimeQ[2 # + 1] &]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



