cp's OEIS Frontend

A342048 Numbers for which the sum of digits equals the product of nonzero digits.

%I A342048 #14 Feb 28 2021 18:52:00
%S A342048 1,2,3,4,5,6,7,8,9,10,20,22,30,40,50,60,70,80,90,100,123,132,200,202,
%T A342048 213,220,231,300,312,321,400,500,600,700,800,900,1000,1023,1032,1124,
%U A342048 1142,1203,1214,1230,1241,1302,1320,1412,1421,2000,2002,2013,2020,2031,2103,2114,2130,2141,2200
%N A342048 Numbers for which the sum of digits equals the product of nonzero digits.
%H A342048 Robert Israel, <a href="/A342048/b342048.txt">Table of n, a(n) for n = 1..10000</a>
%e A342048 2103 is in the sequence because 2 + 1 + 0 + 3 = 2 * 1 * 3 = 6.
%p A342048 q:= n-> (l-> is(add(i, i=l)=mul(i, i=l)))(
%p A342048         subs(0=[][], convert(n, base, 10))):
%p A342048 select(q, [$0..3300])[];  # _Alois P. Heinz_, Feb 26 2021
%p A342048 # alternative
%p A342048 G:= proc(d,dmax,s,p) option remember; local i;
%p A342048    if s + dmax*d < p or s > dmax^d*p then return [] fi;
%p A342048    if d = 0 then return [[]] fi;
%p A342048    [seq(op(map(t -> [i,op(t)], procname(d-1,i,s+i,p*i))),i=1..dmax)]
%p A342048 end proc:
%p A342048 f:= proc(d) local R,k,i;
%p A342048   R:= [seq(op(map(t -> [0$k,op(t)], G(d-k,9,0,1))),k=0..d-1)];
%p A342048   R:= map(op@combinat:-permute,R);
%p A342048   sort(map(t -> add(t[i]*10^(i-1),i=1..d),R))
%p A342048 end proc:
%p A342048 f(4); # _Robert Israel_, Feb 28 2021
%t A342048 Select[Range[2200], Plus @@ IntegerDigits[#] == Times @@ DeleteCases[IntegerDigits[#], 0] &]
%o A342048 (Python)
%o A342048 from math import prod
%o A342048 def ok(n):
%o A342048   digs = list(map(int, str(n)))
%o A342048   return sum(digs) == prod([d for d in digs if d != 0])
%o A342048 def aupto(lim): return [m for m in range(1, lim+1) if ok(m)]
%o A342048 print(aupto(2200)) # _Michael S. Branicky_, Feb 26 2021
%o A342048 (PARI) isok(k) = my(d=select(x->(x>0), digits(k))); vecprod(d) == vecsum(d); \\ _Michel Marcus_, Feb 26 2021
%Y A342048 Cf. A007953, A034710, A051801.
%K A342048 nonn,base
%O A342048 1,2
%A A342048 _Ilya Gutkovskiy_, Feb 26 2021