A361349 Numbers k such that A361338(k) = 10.

17117, 17727, 17749, 18839, 19933, 21761, 22777, 29391, 30397, 31157, 31317, 31643, 33949, 34199, 35909, 39723, 39789, 39797, 39803, 39813, 42973, 44219, 44517, 46347, 47463, 49171, 49771, 49877, 53211, 53751, 57169, 57311, 57769, 57781, 57941, 57943, 57961, 59093

Offset: 1

Author

N. J. A. Sloane, Apr 05 2023

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A361338, A361341-A361348.

Programs

Python

from itertools import count, islice
from math import prod
def A361338(n):
    c, d, m = {n}, set(), 0
    while True:
        c = set(prod(divmod(k,s)) for k in c for i in range(1,len(str(k))) if k%(s:=(r:=10**(i-1))*10)>=r or i==1)
        d |= c
        if (r:=len(d)) == m:
            return sum(1 for q in d if q<10)
        m = r
def A361349_gen(startvalue=1): # generator of terms >= startvalue
    return filter(lambda n:A361338(n)==10,count(max(startvalue,1)))
A361349_list = list(islice(A361349_gen(),10)) # Chai Wah Wu, Apr 05-06 2023

Python

from functools import lru_cache
from itertools import count, islice
@lru_cache(maxsize=None)
def f(n):
    if n < 10: return {n}
    s = str(n)
    return {e for i in range(1, len(s)) if s[i]!="0" or i==len(s)-1 for e in f(int(s[:i])*int(s[i:]))}
def agen(): # generator of terms
    yield from (k for k in count() if len(f(k)) == 10)
print(list(islice(agen(), 38))) # Michael S. Branicky, Apr 05 2023

Extensions

a(4)-a(38) from Chai Wah Wu, Apr 05 2023