A272436 Semiprimes such that sum of digits equals product of digits.

4, 6, 9, 22, 123, 213, 321, 1142, 1214, 1241, 4121, 11215, 11521, 12115, 12151, 21151, 22121, 51211, 111261, 112611, 116121, 116211, 121161, 162111, 211611, 261111, 621111, 1111217, 1111413, 1111431, 1111721, 1112117, 1117121, 1117211, 1121117, 1121171, 1121711

Offset

1,1

Comments

Intersection of A001358 and A034710.

9 is the only member with digit 9. No member has more than one digit 3 or 6. - Robert Israel, May 06 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..17009 (n = 1..3104 from Robert Israel)

Example

1142 appears in the list because 1142 = 2*571 that is semiprime. Also, 1+1+4+2 = 8 = 1*1*4*2.
11215 appears in the list because 1142 = 5*2243 that is semiprime. Also, 1+1+2+1+5 = 10 = 1*1*2*1*5.

Maple

R:= proc(k, d, u, v) option remember;
    if k = 1 then
        if d = v - u then {[d]}
        else {}
        fi
    else
      `union`(seq(map(t -> [op(t), s], procname(k-1, d-s, u+s*k, v*k^s)), s=0..d))
    fi
end proc:
A034710:= proc(d)
  local res, r,  i, t;
  res:= NULL;
  for r in R(9, d, 0, 1) do
     res:= res, op(map(t -> add(10^(i-1)*t[i], i=1..nops(t)), combinat:-permute([seq(i$r[i], i=1..9)])));
  od:
  sort([res]);
end proc:
map(op, [seq(select(t -> numtheory:-bigomega(t)=2, A034710(i)), i=1..11)]); # Robert Israel, May 06 2016

Mathematica

Select[Range[10000000], (Plus @@ IntegerDigits[#]) == (Times @@ IntegerDigits[#]) && PrimeOmega[#] == 2 &]

Crossrefs

Cf. A001358, A034710, A066306, A066307.

Sequence in context: A196104 A046376 A229129 * A338309 A246569 A368648

Adjacent sequences: A272433 A272434 A272435 * A272437 A272438 A272439

Keyword

nonn,base

Author

K. D. Bajpai, May 06 2016

Status

approved