A173082 Semiprimes q such that q^2+2 and q^2-2 are also semiprimes.

6, 51, 65, 115, 133, 141, 159, 187, 201, 209, 213, 287, 291, 295, 327, 339, 361, 407, 411, 413, 471, 493, 511, 519, 537, 559, 579, 597, 633, 649, 687, 695, 723, 799, 813, 831, 835, 871, 917, 939, 1007, 1041, 1047, 1079, 1135, 1167, 1189, 1195, 1199, 1227

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Formula

{A001358(j): A074985(j)-2 in A001358 and A074985(j)+2 in A001358}. [R. J. Mathar, Mar 11 2010]

Example

6^2-2=34 = 2*17 and 6^2+2=38 = 2*19 are semiprimes derived from the semiprime q=6, so q=6 is in the sequence.

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n], a=n^2-2; b=n^2+2; If[f[a]&&f[b], AppendTo[lst, n]]], {n, 8!}]; lst

Crossrefs

Cf. A001358

Sequence in context: A043084 A335704 A292818 * A113653 A133395 A341424

Adjacent sequences: A173079 A173080 A173081 * A173083 A173084 A173085

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 09 2010

Extensions

Definition rephrased - R. J. Mathar, Mar 11 2010

Status

approved