cp's OEIS Frontend

A365009 Semiprimes that are the concatenation of two or more semiprimes.

%I A365009 #15 Aug 24 2023 10:16:48
%S A365009 46,49,69,94,106,146,159,214,219,226,254,259,334,339,346,386,394,415,
%T A365009 422,446,451,458,466,469,482,485,493,514,519,554,559,579,586,589,614,
%U A365009 622,626,629,633,634,635,649,655,662,669,674,685,687,694,695,699,746,749,779,866,869,879,914,921,922
%N A365009 Semiprimes that are the concatenation of two or more semiprimes.
%C A365009 Conjecture: The fraction of semiprimes <= N that are in this sequence goes to 1 as N -> infinity.  What is the first N for which that fraction >= 1/2?
%H A365009 Robert Israel, <a href="/A365009/b365009.txt">Table of n, a(n) for n = 1..10000</a>
%e A365009 a(3) = 69 is a term because 69 = 3 * 23 is a semiprime and is the concatenation of the semiprimes 6 = 2 * 3 and 9 = 3 * 3.
%p A365009 filter:= proc(n) local d,v;
%p A365009   if numtheory:-bigomega(n) <> 2 then return false fi;
%p A365009   for d from 1 to length(n)-1 do
%p A365009      v:= n  mod 10^d;
%p A365009      if v >= 10^(d-1) and numtheory:-bigomega(v)=2 and g((n-v)/10^d) then return true fi
%p A365009   od;
%p A365009   false
%p A365009 end proc:
%p A365009 g:= proc(n) local d,v; option remember;
%p A365009   if numtheory:-bigomega(n) = 2 then return true fi;
%p A365009   for d from 1 to length(n)-1 do
%p A365009     v:= n mod 10^d;
%p A365009     if v >= 10^(d-1) and numtheory:-bigomega(v)=2 and procname((n-v)/10^d) then return true fi
%p A365009   od;
%p A365009   false
%p A365009 end proc:
%p A365009 select(filter, [$10..1000]);
%Y A365009 Cf. A001358, A001238, A019549. Contains A107342.
%K A365009 base,nonn
%O A365009 1,1
%A A365009 _Zak Seidov_ and _Robert Israel_, Aug 15 2023