cp's OEIS Frontend

A217186 a(n) is the number of digits in the decimal representation of the smallest power of 3 that contains n consecutive identical digits.

%I A217186 #13 Mar 12 2025 18:42:32
%S A217186 1,6,16,16,131,257,1014,3684,10875,51142,51142,304989
%N A217186 a(n) is the number of digits in the decimal representation of the smallest power of 3 that contains n consecutive identical digits.
%C A217186 Number of digits in 3^k is equal to floor(1 + k*log_10(3)).
%t A217186 k = 0; Join[{1}, Table[While[d = IntegerDigits[3^k]; prt = Partition[Differences[d], n - 1, 1]; ! MemberQ[prt, Table[0, {n - 1}]], k++]; Length[d], {n, 2, 8}]] (* _T. D. Noe_, Oct 03 2012 *)
%o A217186 (Python)
%o A217186 def A217186(n):
%o A217186     l, x = [str(d)*n for d in range(10)], 1
%o A217186     for m in range(10**9):
%o A217186         s = str(x)
%o A217186         for k in l:
%o A217186             if k in s:
%o A217186                 return len(s)
%o A217186         x *= 3
%o A217186     return 'search limit reached'
%o A217186 # _Chai Wah Wu_, Dec 17 2014
%Y A217186 Cf. A215727, A215733.
%K A217186 nonn,base,more
%O A217186 1,2
%A A217186 _V. Raman_, Sep 27 2012
%E A217186 a(12) from _Chai Wah Wu_, Dec 17 2014