OFFSET
1,1
COMMENTS
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?
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
MAPLE
filter:= proc(n) local d, v;
if numtheory:-bigomega(n) <> 2 then return false fi;
for d from 1 to length(n)-1 do
v:= n mod 10^d;
if v >= 10^(d-1) and numtheory:-bigomega(v)=2 and g((n-v)/10^d) then return true fi
od;
false
end proc:
g:= proc(n) local d, v; option remember;
if numtheory:-bigomega(n) = 2 then return true fi;
for d from 1 to length(n)-1 do
v:= n mod 10^d;
if v >= 10^(d-1) and numtheory:-bigomega(v)=2 and procname((n-v)/10^d) then return true fi
od;
false
end proc:
select(filter, [$10..1000]);
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Zak Seidov and Robert Israel, Aug 15 2023
STATUS
approved