cp's OEIS Frontend

A242605 Start of a triple of consecutive squarefree numbers which are all semiprimes.

%I A242605 #24 Jan 19 2019 04:15:43
%S A242605 33,55,85,91,93,115,118,119,141,142,143,158,201,202,203,205,213,214,
%T A242605 215,217,218,295,298,299,301,302,323,326,391,393,411,413,445,451,511,
%U A242605 514,535,542,551,622,633,685,694,695,697,745,763,778,791,799,815,842,843,865,898,921,922
%N A242605 Start of a triple of consecutive squarefree numbers which are all semiprimes.
%C A242605 Sequence A039833 is a subsequence.
%H A242605 Harvey P. Dale, <a href="/A242605/b242605.txt">Table of n, a(n) for n = 1..1000</a>
%H A242605 Daniel C. Mayer, <a href="http://www.linkedin.com/groupItem?view=&amp;gid=4510047&amp;item=5873010790079934468&amp;type=member">Define an "m-triple" to consist of three consecutive squarefree positive integers, each with exactly m prime divisors</a>, Number Theory group on LinkedIn.com
%e A242605 33 is in the sequence because 33, 34, 35 are all squarefree semiprimes.
%e A242605 55 is in the sequence because 55, 57, 58 (we ignore 56 because it's not squarefree) are all squarefree semiprimes.
%t A242605 Transpose[Select[Partition[Select[Range[1000],SquareFreeQ],3,1], Union[ PrimeOmega[ #]] =={2}&]][[1]] (* _Harvey P. Dale_, Feb 07 2016 *)
%o A242605 (PARI) is_A242605(n,c=2)==issquarefree(n)&&omega(n)==2&&(!c||until(issquarefree(n++),)||is_A242605(n,c-1))
%o A242605 (PARI) (back(n,c=1)=until(issquarefree(n--)&&c--,);n); for(n=1,999,issquarefree(n)||next;dk==4&&dk==dm&&numdiv(n)==dm&&print1(back(n)",");dk=dm;dm=numdiv(n))
%Y A242605 Cf. A242606 (m=3), A242607 (m=4), A242608 (m=5), A242621 (first terms for positive m).
%K A242605 nonn
%O A242605 1,1
%A A242605 _M. F. Hasler_, May 18 2014