A277356 Jacobsthal numbers which are semiprimes.

21, 85, 341, 5461, 22369621, 178956971, 5726623061, 45812984491, 91625968981, 733007751851, 46912496118443, 187649984473771, 3002399751580331, 1537228672809129301, 49191317529892137643, 787061080478274202283, 3148244321913096809131

Offset: 1

Author

Ilya Gutkovskiy, Oct 10 2016

Keywords

• nonn

Comments

Semiprimes of the form (2^k - (-1)^k)/3.

Examples

			a(1) = 21 because 21 = 3*7 = (2^6 - (-1)^6)/3, so 21 is semiprime as well as a Jacobsthal number;
a(2) = 85 because 85 = 5*17 = (2^8 - (-1)^8)/3;
a(3) = 341 because 341 = 11*31 = (2^10 - (-1)^10)/3, etc.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..49
• Eric Weisstein's World of Mathematics, Jacobsthal Number.
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A001045, A001358, A049883, A363837.

Programs

Mathematica

Select[Table[(2^k - (-1)^k)/3, {k, 100}], PrimeOmega[#1] == 2 & ]

Formula

a(n) = A001045(A363837(n)). - Amiram Eldar, Feb 25 2024