Longest run of the digit S000167(n) in the decimal form of 2^n.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 2, 3, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 3, 3, 4, 3, 3, 3, 3, 2, 2, 1, 2, 3, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 1, 2, 2, 3, 2, 2, 2
0
For the first number n producing a given run of digits, see A045875. Sequence A215732 lists the digit that is repeated.
T. D. Noe, Plot of 1001 terms
T. D. Noe, Table of 1001 terms
(Mma) t = Table[s = Sort[Split[IntegerDigits[2^n]]]; len = Length[s[[-1]]]; u = Flatten[Select[s, Length[#] == len &, 1]]; {u[[1]], Length[u]}, {n, 0, 100}]; Transpose[t][[2]]
Cf. S000165-S000167, A045875, A215732.
nonn,base
T. D. Noe, Jul 25 2014