A128290 If p(x) is the product of the digits of the number x and s(x) the sum of the digits then the sequence lists all the numbers k for which p(s(k)) = s(p(k)), with k >= 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 36, 63, 109, 123, 132, 158, 185, 190, 199, 208, 213, 231, 280, 289, 298, 307, 312, 321, 333, 370, 406, 458, 460, 469, 485, 496, 505, 518, 548, 550, 556, 559, 565, 581, 584, 595, 604, 640, 649, 655, 667, 676, 694, 703, 730, 766, 802

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

496 is a term: s(496) = 4+9+6 = 19, p(s(496)) = 1*9 = 9, p(496) = 4*9*6 = 216, s(p(496)) = 2+1+6 = 9.
845 is a term: s(845) = 8+4+5 = 17, p(s(845)) = 1*7 = 7, p(845) = 8*4*5 = 160, s(p(845)) = 1+6+0 = 7.
From Jon E. Schoenfield, Jun 15 2024: (Start)
Expressed more visually:
.
          Sum                         Sum
   496 --------> 19            845 --------> 17
    |    4+9+6    |             |    8+4+5    |
  P | 4         P |           P | 8         P |
  r | *         r | 1         r | *         r | 1
  o | 9         o | *         o | 4         o | *
  d | *         d | 9         d | *         d | 7
    | 6           |             | 5           |
    v     Sum     v             v     Sum     v
   216 -------->  9            160 -------->  7
         2+1+6                       1+6+0
(End)

Maple

P:=proc(q) local a, b, c; a:=convert(q, base, 10): b:=convert(a, `+`): c:=convert(a, `*`):
if convert(convert(b, base, 10), `*`)=convert(convert(c, base, 10), `+`) then q; fi; end: seq(P(i), i=1..10^3); # Paolo P. Lava, Jun 15 2024

Mathematica

p[n_] := Times @@ IntegerDigits[n]; Select[Range[1000], p[DigitSum[#]] == DigitSum[p[#]] &] (* Paolo Xausa, Jun 17 2024 *)

Prog

(Python)
from math import prod
def ok(n):
    d = list(map(int, str(n)))
    p, s = prod(d), sum(d)
    return sum(map(int, str(p))) == prod(map(int, str(s)))
print([k for k in range(1, 803) if ok(k)]) # Michael S. Branicky, Jun 15 2024

Crossrefs

Cf. A007953, A007954.

Sequence in context: A037264 A274124 A045910 * A110002 A232709 A249334

Adjacent sequences: A128287 A128288 A128289 * A128291 A128292 A128293

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, May 04 2007

Status

approved