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

Author

Malo David, Nov 09 2021

Keywords

• nonn
• base
• more

Comments

a(12) > 10^22 if it exists. - Max Alekseyev, Jan 19 2025

Examples

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

Crossrefs

Cf. A055642, A349194, A349279.

Programs

Mathematica

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

PARI

isok(k) = {my(d=digits(k)); prod(i=1, #d, sum(j=1, i, d[j])) == k;} \\ Michel Marcus, Nov 10 2021

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=", ")

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