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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A039547 A029704 A260835 * A264352 A044252 A044633

Adjacent sequences: A173084 A173085 A173086 * A173088 A173089 A173090

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

Extensions

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

Status

approved