A085722 Numbers k such that k^2 + 1 is a semiprime.

3, 5, 8, 9, 11, 12, 15, 19, 22, 25, 28, 29, 30, 34, 35, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 58, 59, 60, 61, 62, 64, 65, 69, 71, 76, 78, 79, 80, 85, 86, 88, 92, 95, 96, 100, 101, 102, 104, 106, 108, 114, 121, 131, 136, 139, 140, 141, 144, 145, 152, 154, 158, 159, 164

Offset: 1

Author

Jason Earls, Jul 20 2003

Keywords

• easy
• nonn

Comments

Corresponding semiprimes k^2+1 are in A144255.

Solutions to the equation: A000005(1+k^2) = 4. - Enrique Pérez Herrero, May 03 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A014442, A089120, A144255, A193432.

Programs

Mathematica

lst={}; Do[If[Plus@@Last/@FactorInteger[n^2+1]==2, AppendTo[lst,n]], {n,0,200}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 24 2009 *)
Select[Range[200],PrimeOmega[#^2+1]==2&] (* Harvey P. Dale, Feb 28 2013 *)

PARI

select(vector(50,n,n),n->bigomega(n^2+1)==2)
\\ Zak Seidov, Feb 25 2011

Formula

A085722 = A193432^-1({2}). - M. F. Hasler, Mar 11 2012