A248201 Numbers n such that n-1, n and n+1 are all squarefree semiprimes.

34, 86, 94, 142, 202, 214, 218, 302, 394, 446, 634, 698, 922, 1042, 1138, 1262, 1346, 1402, 1642, 1762, 1838, 1894, 1942, 1982, 2102, 2182, 2218, 2306, 2362, 2434, 2462, 2518, 2642, 2722, 2734, 3098, 3386, 3602, 3694, 3866, 3902, 3958, 4286, 4414

Offset: 1

Author

James G. Merickel, Oct 03 2014

Keywords

• nonn

Comments

A subsequence of A169834. - M. F. Hasler, Oct 26 2014

Examples

			33, 34 and 35 factor as 3*11, 2*17 and 5*7, respectively.  No smaller such trio exists, so a(1)=34.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Wikipedia, Semiprime

Crossrefs

Cf. A006881, A039833, A169834, A195685, A248202, A248203, A248204, A259349, A259350, A259801.

Programs

Mathematica

lst={}; Do[z=n^3 + 3 n^2 + 2 n; If[PrimeOmega[z/n]==PrimeOmega[z/(n + 2)]==4 && PrimeNu[z]==6, AppendTo[lst, n + 1]], {n, 1, 6000, 2}]; lst (* Vincenzo Librandi, Jul 24 2015 *)
SequencePosition[Table[If[SquareFreeQ[n]&&PrimeOmega[n]==2,1,0],{n,4500}],{1,1,1}][[All,1]]+1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 11 2018 *)

PARI

sq(n)=bigomega(n)==2 && omega(n)==2;
for(n=3,10^4,if(sq(n-1)&&sq(n)&&sq(n+1),print1(n,", ")));
\\ Joerg Arndt, Oct 18 2014

Formula

a(n) = A039833(n) + 1. - Michel Marcus, Oct 25 2014

a(n) = 2 * A195685(n). - Torlach Rush, Jun 25 2021