cp's OEIS Frontend

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.

%I A349190 #79 Jan 19 2025 12:05:33
%S A349190 1,2,3,4,5,6,7,8,9,48,24192
%N 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.
%C A349190 a(12) > 10^22 if it exists. - _Max Alekseyev_, Jan 19 2025
%e A349190 24192 is a term since 24192 = 2*(2+4)*(2+4+1)*(2+4+1+9)*(2+4+1+9+2).
%t A349190 Select[Range[10^5],Times@@Total/@Table[IntegerDigits[#][[;;k]],{k,IntegerLength@#}]==#&] (* _Giorgos Kalogeropoulos_, Nov 10 2021 *)
%o A349190 (Python)
%o A349190 def main(N): # prints all terms <= N
%o A349190   for k in range(1,N+1):
%o A349190     n1=str(k)
%o A349190     n2 = 1
%o A349190     for i in range(1,len(n1)+1):
%o A349190       sum1 = 0
%o A349190       for j in range(0,i):
%o A349190         sum1 += int(n1[j])
%o A349190       n2 = n2*sum1
%o A349190     if n2 == k:
%o A349190        print(k, end=", ")
%o A349190 (PARI) isok(k) = {my(d=digits(k)); prod(i=1, #d, sum(j=1, i, d[j])) == k;} \\ _Michel Marcus_, Nov 10 2021
%o A349190 (Python)
%o A349190 from itertools import islice, accumulate, count
%o A349190 from math import prod
%o A349190 def A349190gen(): return filter(lambda n:prod(accumulate(int(d) for d in str(n))) == n,count(1)) # generator of terms
%o A349190 A349190_list = list(islice(A349190gen(),11)) # _Chai Wah Wu_, Dec 02 2021
%Y A349190 Cf. A055642, A349194, A349279.
%K A349190 nonn,base,more
%O A349190 1,2
%A A349190 _Malo David_, Nov 09 2021