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A365009
Semiprimes that are the concatenation of two or more semiprimes.
1
46, 49, 69, 94, 106, 146, 159, 214, 219, 226, 254, 259, 334, 339, 346, 386, 394, 415, 422, 446, 451, 458, 466, 469, 482, 485, 493, 514, 519, 554, 559, 579, 586, 589, 614, 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
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
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
Cf. A001358, A001238, A019549. Contains A107342.
Sequence in context: A098194 A181460 A235687 * A321046 A269671 A039354
KEYWORD
base,nonn
AUTHOR
Zak Seidov and Robert Israel, Aug 15 2023
STATUS
approved