A242330 Numbers k such that k^2 + 2 is a semiprime.

2, 6, 7, 11, 12, 17, 18, 27, 29, 35, 37, 42, 43, 48, 51, 53, 54, 55, 60, 65, 66, 69, 72, 73, 75, 79, 83, 84, 87, 90, 93, 97, 115, 119, 125, 132, 133, 135, 137, 141, 144, 150, 153, 155, 159, 161, 165, 169, 174, 183, 186, 187, 189, 191, 192, 195, 198

Offset: 1

Author

Vincenzo Librandi, May 14 2014

Keywords

• nonn
• easy

Comments

The semiprimes of this form are: 6, 38, 51, 123, 146, 291, 326, 731, 843, 1227, 1371, 1766, 1851, 2306, 2603, 2811, 2918, 3027, 3602, ....

There are no four consecutive terms in this sequence, that is, a(n) > a(n-3) + 3 (check mod 6). Probably sieve theory can show that this sequence has density 0. - Charles R Greathouse IV, Feb 24 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A056899, A067201, A085722, A242331, A242332, A242333.

Programs

Magma

IsSemiprime:=func; [n: n in [2..200] | IsSemiprime(s) where s is n^2+2];

Mathematica

Select[Range[300], PrimeOmega[#^2 + 2] == 2 &]

PARI

issemi(n)=forprime(p=2,997,if(n%p==0, return(isprime(n/p)))); bigomega(n)==2
is(n)=issemi(n^2+2) \\ Charles R Greathouse IV, Feb 24 2023

Formula

a(n) > 2n for n > 1. - Charles R Greathouse IV, Feb 24 2023