cp's OEIS Frontend

A243150 Least number k > 0 such that 2^k contains an n-digit long substring of the infinite string "0123456789012345678901234567890123456....".

%I A243150 #12 May 05 2025 16:39:12
%S A243150 1,7,28,106,391,992,1178,7255,15975,67143,333212,333212,1641257
%N A243150 Least number k > 0 such that 2^k contains an n-digit long substring of the infinite string "0123456789012345678901234567890123456....".
%C A243150 By A238448, a(10) <= 244178.
%e A243150 2^7 = 128 contains the 2-digit substring "12". Thus a(2) = 7.
%o A243150 (Python)
%o A243150 import sys
%o A243150 sys.set_int_max_str_digits(5000)
%o A243150 def a(n):
%o A243150   for k in range(1, 10**5):
%o A243150     for i in range(10):
%o A243150       s = ''
%o A243150       for j in range(i, i+n):
%o A243150         dig=j%10
%o A243150         s+=str(dig)
%o A243150       if str(2**k).find(s) > -1:
%o A243150         return k
%o A243150 n=1
%o A243150 while n < 10:
%o A243150   print(a(n))
%o A243150   n+=1
%Y A243150 Cf. A238448.
%K A243150 nonn,more,hard,base
%O A243150 1,2
%A A243150 _Derek Orr_, May 31 2014
%E A243150 a(10)-a(13) from _Hiroaki Yamanouchi_, Sep 26 2014