A173085 -id:A173085 - cp's OEIS frontend

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

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

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

Cf. A001358, A173082, A173083, A173084, A173085

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

Edited by Charles R Greathouse IV, Apr 06 2010

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

Original entry on oeis.org

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

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

nonn

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

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

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

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

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 *)

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

cp's OEIS Frontend

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

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