A383971 Triprimes with sum of digits 3.

12, 30, 102, 1002, 2001, 10002, 10011, 11001, 20001, 100101, 101001, 110001, 200001, 1000002, 10001001, 10010001, 11000001, 20000001, 100000101, 1000000011, 1000001001, 1000010001, 1000100001, 1001000001, 1010000001, 10000000002, 10000000011, 10000010001, 11000000001, 100000000101, 100000001001

Offset: 1

Author

Robert Israel, May 16 2025

Keywords

• nonn
• base

Comments

Numbers that are the product of 3 primes, counted with multiplicity, and whose sum of decimal digits is 3.

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.

For each d from 2 to at least 71, there is at least one term with d digits.

Includes 10^k + 2 for k in A076850.

All terms except 12 are squarefree.

All even terms are Zumkeller numbers (A083207). - Ivan N. Ianakiev, May 18 2025

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..380

Crossrefs

Intersection of any two of A014612, A050689, and A052217.

Cf. A001222, A007953, A076850, A083207.

Programs

Maple

istriprime:= proc(n) local F;
  F:= ifactors(n,easy)[2];
  if not hastype(F,symbol) then return convert(F[..,2],`+`)=3 fi;
  F:= remove(hastype,F,symbol);
  if nops(F) > 1 or (nops(F) = 1 and F[1,2] > 1) then return false fi;
  numtheory:-bigomega(n) = 3
end proc:
R:= 12, 30:
for d from 3 to 30 do
  V:= select(istriprime, [seq(seq(10^(d-1) + 10^j + 1,j=0..d-1)]);
  R:= R,op(V);
od:
R;

Mathematica

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 *)