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

%I A361349 #20 Apr 06 2023 10:38:05
%S A361349 17117,17727,17749,18839,19933,21761,22777,29391,30397,31157,31317,
%T A361349 31643,33949,34199,35909,39723,39789,39797,39803,39813,42973,44219,
%U A361349 44517,46347,47463,49171,49771,49877,53211,53751,57169,57311,57769,57781,57941,57943,57961,59093
%N A361349 Numbers k such that A361338(k) = 10.
%H A361349 Michael S. Branicky, <a href="/A361349/b361349.txt">Table of n, a(n) for n = 1..10000</a>
%o A361349 (Python)
%o A361349 from itertools import count, islice
%o A361349 from math import prod
%o A361349 def A361338(n):
%o A361349     c, d, m = {n}, set(), 0
%o A361349     while True:
%o A361349         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)
%o A361349         d |= c
%o A361349         if (r:=len(d)) == m:
%o A361349             return sum(1 for q in d if q<10)
%o A361349         m = r
%o A361349 def A361349_gen(startvalue=1): # generator of terms >= startvalue
%o A361349     return filter(lambda n:A361338(n)==10,count(max(startvalue,1)))
%o A361349 A361349_list = list(islice(A361349_gen(),10)) # _Chai Wah Wu_, Apr 05-06 2023
%o A361349 (Python)
%o A361349 from functools import lru_cache
%o A361349 from itertools import count, islice
%o A361349 @lru_cache(maxsize=None)
%o A361349 def f(n):
%o A361349     if n < 10: return {n}
%o A361349     s = str(n)
%o A361349     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:]))}
%o A361349 def agen(): # generator of terms
%o A361349     yield from (k for k in count() if len(f(k)) == 10)
%o A361349 print(list(islice(agen(), 38))) # _Michael S. Branicky_, Apr 05 2023
%Y A361349 Cf. A361338, A361341-A361348.
%K A361349 nonn,base
%O A361349 1,1
%A A361349 _N. J. A. Sloane_, Apr 05 2023
%E A361349 a(4)-a(38) from _Chai Wah Wu_, Apr 05 2023