A349190 Numbers k such that k equals the product of the sum of its first i digits, with i going from 1 to the total number of digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 48, 24192

Offset

1,2

Comments

a(12) > 10^10 if it exists. - David A. Corneth, Nov 10 2021

a(12) > 10^11 if it exists. - Malo David, Nov 15 2021

a(12) > 10^17 if it exists. - Jon E. Schoenfield, Nov 28 2021

Links

Table of n, a(n) for n=1..11.

Example

24192 is a term since 24192 = 2*(2+4)*(2+4+1)*(2+4+1+9)*(2+4+1+9+2).

Mathematica

Select[Range[10^5], Times@@Total/@Table[IntegerDigits[#][[;; k]], {k, IntegerLength@#}]==#&] (* Giorgos Kalogeropoulos, Nov 10 2021 *)

Prog

(Python)
def main(N): # prints all terms <= N
  for k in range(1, N+1):
    n1=str(k)
    n2 = 1
    for i in range(1, len(n1)+1):
      sum1 = 0
      for j in range(0, i):
        sum1 += int(n1[j])
      n2 = n2*sum1
    if n2 == k:
       print(k, end=", ")
(PARI) isok(k) = {my(d=digits(k)); prod(i=1, #d, sum(j=1, i, d[j])) == k; } \\ Michel Marcus, Nov 10 2021
(Python)
from itertools import islice, accumulate, count
from math import prod
def A349190gen(): return filter(lambda n:prod(accumulate(int(d) for d in str(n))) == n, count(1)) # generator of terms
A349190_list = list(islice(A349190gen(), 11)) # Chai Wah Wu, Dec 02 2021

Crossrefs

Cf. A055642, A349194.

Sequence in context: A219327 A219326 A335205 * A252781 A024660 A257814

Adjacent sequences: A349187 A349188 A349189 * A349191 A349192 A349193

Keyword

nonn,base,more

Author

Malo David, Nov 09 2021

Status

approved