login
A248201
Numbers n such that n-1, n and n+1 are all squarefree semiprimes.
9
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
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
KEYWORD
nonn
AUTHOR
James G. Merickel, Oct 03 2014
STATUS
approved