cp's OEIS Frontend

A243295 Least number k > 0 such that 3^k contains an n-digit long substring of the infinite string "0123456789012345678901234567890123456...".

%I A243295 #26 Jul 23 2025 11:20:00
%S A243295 1,8,15,57,102,332,2345,2345,10110,118745,127188,326758,2258910,
%T A243295 6154926
%N A243295 Least number k > 0 such that 3^k contains an n-digit long substring of the infinite string "0123456789012345678901234567890123456...".
%C A243295 a(n) is an increasing (but not necessarily strictly increasing) sequence.
%C A243295 a(7) = 4849 if all numbers were distinct.
%C A243295 By A238507, a(10) <= 200633.
%C A243295 a(15) > 10^7. - _Delbert L. Johnson_, Apr 13 2024
%e A243295 3^8 = 6561 contains a subsequence of the infinite string in the definition ('56'). Thus a(2) = 8.
%o A243295 (Python)
%o A243295 def a(n):
%o A243295   for k in range(1, 10**5):
%o A243295     for i in range(10):
%o A243295       s = ''
%o A243295       for j in range(i, i+n):
%o A243295         dig=j%10
%o A243295         s+=str(dig)
%o A243295       if str(3**k).find(s) > -1:
%o A243295         return k
%o A243295 n=1
%o A243295 while n < 10:
%o A243295   print(a(n))
%o A243295   n+=1
%Y A243295 Cf. A238507.
%K A243295 nonn,hard,base,more
%O A243295 1,2
%A A243295 _Derek Orr_, Jun 02 2014
%E A243295 a(10)-a(12) from _Hiroaki Yamanouchi_, Sep 26 2014
%E A243295 a(13) from _Chai Wah Wu_, Jun 14 2020
%E A243295 a(14) from _Delbert L. Johnson_, Apr 13 2024