A217185 a(n) is the number of digits in the decimal representation of the smallest power of 2 that contains n consecutive identical digits.

1, 5, 8, 13, 67, 293, 293, 2576, 12790, 12790, 81874, 312865, 520061, 2063822

Offset: 1

Author

V. Raman, Sep 27 2012

Keywords

• nonn
• base

Comments

Number of digits in 2^k is equal to floor(1 + k*log_10(2)).

Crossrefs

Cf. A045875, A215732.

Programs

Mathematica

k = 0; Join[{1}, Table[While[d = IntegerDigits[2^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 *)