Position of first zero digit in 2^n, counting from the right.
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0, 0, 3, 0, 0, 6, 6, 2, 2, 0, 0, 5, 0, 0, 4, 9, 0, 0, 0, 0, 0, 0, 0, 5, 0, 12, 9, 2, 2, 6, 6, 13, 13, 4, 0, 8, 0, 4, 4, 8, 9, 9, 9, 13, 8, 8, 11, 2, 2, 8, 5, 5, 0, 14, 8, 5, 5, 0, 7, 7, 5, 0, 0, 14, 3, 5, 0, 2, 2, 12
0
Zero indicates that there are no zeros in the number. Is there a maximum value for this function? This question was discussed in MathOverflow. Sequence A031141 lists the maximum values minus one.
T. D. Noe, Plot of 10001 terms
T. D. Noe, Table of 10001 terms
MathOverflow, Zeros in the representation of powers of 3
(Mma) Table[s = Position[Reverse[IntegerDigits[2^n]], 0]; If[Length[s] == 0, 0, s[[1, 1]]], {n, 0, 100}]
Cf. A007277 (n for which there are no zeros), A031140 (position of record values), A031141.
Cf. S000287-S000293.
nonn,base
T. D. Noe, Oct 12 2014