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

1,1

Comments

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

Links

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

Wikipedia, Semiprime

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A365200 A086005 A169834 * A140602 A067977 A183311

Adjacent sequences: A248198 A248199 A248200 * A248202 A248203 A248204

Keyword

nonn

Author

James G. Merickel, Oct 03 2014

Status

approved