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A383971 Triprimes with sum of digits 3.

%I A383971 #27 Jun 01 2025 10:06:43
%S A383971 12,30,102,1002,2001,10002,10011,11001,20001,100101,101001,110001,
%T A383971 200001,1000002,10001001,10010001,11000001,20000001,100000101,
%U A383971 1000000011,1000001001,1000010001,1000100001,1001000001,1010000001,10000000002,10000000011,10000010001,11000000001,100000000101,100000001001
%N A383971 Triprimes with sum of digits 3.
%C A383971 Numbers that are the product of 3 primes, counted with multiplicity, and whose sum of decimal digits is 3.
%C A383971 Since all terms are divisible by 3, the only term ending with 0 is 30. All others are of the form 10^i + 10^j + 1 with 0 <= j <= i.
%C A383971 For each d from 2 to at least 71, there is at least one term with d digits.
%C A383971 Includes 10^k + 2 for k in A076850.
%C A383971 All terms except 12 are squarefree.
%C A383971 All even terms are Zumkeller numbers (A083207). - _Ivan N. Ianakiev_, May 18 2025
%H A383971 Robert Israel, <a href="/A383971/b383971.txt">Table of n, a(n) for n = 1..380</a>
%e A383971 a(4) = 1002 is a term because 1+0+0+2 = 3 and 1002 = 2 * 3 * 167 is the product of 3 primes, counted with multiplicity.
%p A383971 istriprime:= proc(n) local F;
%p A383971   F:= ifactors(n,easy)[2];
%p A383971   if not hastype(F,symbol) then return convert(F[..,2],`+`)=3 fi;
%p A383971   F:= remove(hastype,F,symbol);
%p A383971   if nops(F) > 1 or (nops(F) = 1 and F[1,2] > 1) then return false fi;
%p A383971   numtheory:-bigomega(n) = 3
%p A383971 end proc:
%p A383971 R:= 12, 30:
%p A383971 for d from 3 to 30 do
%p A383971   V:= select(istriprime, [seq(seq(10^(d-1) + 10^j + 1,j=0..d-1)]);
%p A383971   R:= R,op(V);
%p A383971 od:
%p A383971 R;
%t A383971 s={30};imax=11;Do[n=10^i+10^j+1;If[PrimeOmega[n]==3,AppendTo[s,n]],{i,0,imax},{j,0,i}];Sort[s] (* _James C. McMahon_, Jun 01 2025 *)
%Y A383971 Intersection of any two of A014612, A050689, and A052217.
%Y A383971 Cf. A001222, A007953, A076850, A083207.
%K A383971 nonn,base
%O A383971 1,1
%A A383971 _Robert Israel_, May 16 2025