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A173087 Semiprimes k such that k^2 - 7 and k^2 + 7 are also semiprime. 0

%I

%S 82,142,214,254,326,358,386,478,538,542,566,674,758,802,974,1198,1366,

%T 1466,1594,1754,1762,1942,2302,2342,2374,2582,2654,2746,2762,2818,

%U 2998,3106,3134,3418,3494,3518,3554,3566,3646,3734,3778,3862,4138,4178,4258

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

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

%t 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

%o (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

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

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 09 2010

%E Edited by _Klaus Brockhaus_ and _N. J. A. Sloane_, Feb 25 2010

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Last modified September 19 12:57 EDT 2019. Contains 327198 sequences. (Running on oeis4.)