A173087 Semiprimes k such that k^2 - 7 and k^2 + 7 are also semiprime.

82, 142, 214, 254, 326, 358, 386, 478, 538, 542, 566, 674, 758, 802, 974, 1198, 1366, 1466, 1594, 1754, 1762, 1942, 2302, 2342, 2374, 2582, 2654, 2746, 2762, 2818, 2998, 3106, 3134, 3418, 3494, 3518, 3554, 3566, 3646, 3734, 3778, 3862, 4138, 4178, 4258

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

Keywords

• nonn

Examples

			82 = 2*41, 82^2 - 7 = 6717 = 3*2239 and 82^2 + 7 = 6731 = 53*127 are all semiprime, hence 82 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001358, A173082, A173083, A173084, A173085, A173086.

Programs

Magma

IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [2..4300] | IsSemiprime(n) and IsSemiprime(n^2-7) and IsSemiprime(n^2+7) ]; // Klaus Brockhaus, Feb 25 2010

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1}||Last/@FactorInteger[n]=={2}; lst={};Do[If[f[n], a=n^2-7;b=n^2+7;If[f[a]&&f[b],AppendTo[lst,n]]],{n,8!}];lst
Select[Range[4500],Thread[PrimeOmega[{#,#^2-7,#^2+7}]]=={2,2,2}&] (* Harvey P. Dale, Jul 27 2022 *)

Extensions

Edited by Klaus Brockhaus and N. J. A. Sloane, Feb 25 2010