The digit in the longest run in the decimal form of 7^n; the least one if there are duplicates.
1, 7, 4, 3, 0, 0, 1, 2, 0, 0, 2, 7, 0, 8, 2, 9, 3, 0, 4, 1, 0, 0, 8, 0, 4, 0, 3, 0, 4, 5, 2, 7, 1, 4, 1, 2, 3, 1, 1, 1, 0, 0, 1, 2, 0, 3, 3, 3, 8, 1, 6, 4, 1, 6, 1, 2, 0, 1, 4, 1, 0, 0, 0, 3, 0, 0, 1, 3, 0, 2, 6, 9, 8, 0, 0, 0, 0, 0, 4, 8, 2, 5, 0, 0, 0, 2, 9
0
Sequence S000178 gives the length of the run in 7^n.
T. D. Noe, Plot of 1001 terms
T. D. Noe, Table of 1001 terms
(Mma) t = Table[s = Sort[Split[IntegerDigits[7^n]]]; len = Length[s[[-1]]]; u = Flatten[Select[s, Length[#] == len &, 1]]; {u[[1]], Length[u]}, {n, 0, 100}]; Transpose[t][[1]]
nonn,base
T. D. Noe, Aug 06 2014