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
Keywords
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
Programs
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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
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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