A237039 Semiprimes of the form (2*p)^3 + 1, where p is prime.

65, 217, 10649, 195113, 1191017, 45882713, 55742969, 946966169, 2106997769, 2289529433, 2548895897, 10735357817, 26946035993, 54958685609, 77199941513, 131561576057, 132495001193, 440016501017, 456888832409, 623273556089, 848202406697, 966188398457

Offset: 1

Author

Jonathan Sondow, Feb 02 2014

Keywords

• nonn

Examples

			(2*2)^3 + 1 = 65 = 5*13 is a semiprime, so a(1) = 2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Semiprime.
• Wikipedia, Semiprime.

Crossrefs

Cf. A001358, A046315, A081256, A096173, A096174, A237037, A237038, A237040.

Programs

Mathematica

L = Select[Range[5000], PrimeQ[#] && PrimeQ[(2 #)^2 - 2 # + 1] && PrimeQ[2 # + 1] &]; (2 L)^3 + 1
Select[Table[(2p)^3+1,{p,Prime[Range[1000]]}],PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 21 2021 *)

Formula

a(n) = (2*A237038(n))^3 + 1.