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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.
3
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
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
Sequence in context: A219327 A219326 A335205 * A252781 A024660 A257814
KEYWORD
nonn,base,more
AUTHOR
Malo David, Nov 09 2021
STATUS
approved