A173086 Numbers k such that k, k^2 - 6, and k^2 + 6 are semiprime.

4, 10, 49, 95, 121, 217, 247, 289, 295, 301, 305, 335, 371, 427, 469, 493, 535, 551, 581, 583, 707, 721, 745, 749, 767, 815, 817, 835, 851, 893, 899, 901, 973, 1099, 1169, 1205, 1219, 1253, 1333, 1349, 1379, 1405, 1501, 1603, 1685, 1711, 1739, 1751, 1757, 1765

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

Keywords

• nonn
• changed

Examples

			4=2*2, 4^2-6=10=2*5, 4^2+6=22=2*11, so 4 is in the sequence.
		

Crossrefs

Cf. A001358, A173082, A173083, A173084, A173085

Programs

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1}||Last/@FactorInteger[n]=={2}; lst={};Do[If[f[n], a=n^2-6;b=n^2+6;If[f[a]&&f[b],AppendTo[lst,n]]],{n,8!}];lst

Extensions

Edited by Charles R Greathouse IV, Apr 06 2010