A317138 Numbers k such that (2k)^3 - 1 is a semiprime.

3, 4, 6, 7, 10, 12, 19, 27, 31, 40, 45, 55, 69, 75, 82, 84, 96, 97, 136, 139, 157, 166, 174, 199, 201, 217, 250, 286, 321, 322, 360, 364, 381, 399, 406, 430, 432, 439, 460, 496, 510, 511, 535, 546, 549, 559, 565, 591, 601, 615, 630, 654, 717, 720, 724, 727, 742

Offset

1,1

Comments

Numbers k such that 2k - 1 and 4k^2 + 2k + 1 are both prime.

Links

K. D. Bajpai, Table of n, a(n) for n = 1..9443

Formula

a(n) = A096175(n)/2 = (1/2)*(A242262(n) + 1)^(1/3).

Example

From K. D. Bajpai, Nov 16 2019: (Start)
a(3) = 6 is a term because (2*6)^3 - 1 = 1727 = 11*157, which is a semiprime.
a(4) = 7 is a term because (2*7)^3 - 1 = 2743 = 13*211, which is a semiprime.
9 is not in the sequence because (2*9)^3 - 1 = 5831 = 7*7*7*17, which is not semiprime.
(End)

Maple

issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:
select( n-> issp((2*n)^3-1),  [seq(n, n=1..200)]); # K. D. Bajpai, Nov 16 2019

Mathematica

Select[Range@ 750, PrimeOmega[(2 #)^3 - 1] == 2 &] (* Michael De Vlieger, Aug 02 2018 *)

Prog

(PARI) for(k=1, 500, if(bigomega((2*k)^3-1)==2, print1(k, ", ")))
(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..800] | IsSemiprime(s) where s is (2*n)^3-1]; // Vincenzo Librandi, Aug 04 2018

Crossrefs

Cf. A096175, A242262.

Cf. A237037 (numbers k such that (2k)^3 + 1 is a semiprime).

Sequence in context: A147609 A202169 A239438 * A032387 A026313 A024912

Adjacent sequences: A317135 A317136 A317137 * A317139 A317140 A317141

Keyword

nonn

Author

Jianing Song, Aug 01 2018

Status

approved