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

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

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

Cf. A001358, A001238, A019549. Contains A107342.

Sequence in context: A098194 A181460 A235687 * A321046 A269671 A039354

Adjacent sequences: A365006 A365007 A365008 * A365010 A365011 A365012

Keyword

base,nonn

Author

Zak Seidov and Robert Israel, Aug 15 2023

Status

approved