A277356 Jacobsthal numbers which are semiprimes.

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

Offset

1,1

Comments

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

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.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A001045, A001358, A049883, A363837.

Sequence in context: A374527 A116972 A221475 * A041858 A217549 A063651

Adjacent sequences: A277353 A277354 A277355 * A277357 A277358 A277359

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 10 2016

Status

approved