MathDB

Consider the sequence

\{a_n\}

defined so that

a_n

is the leftmost digit of

2^n

. The first few terms of this sequence are

1,2,4,8,1,3,6,\dots

. For how many

0\le n\le100000

a_n=1

? If

C

is the correct answer and

A

is your answer, then your score will be rounded up from

\max\left(0,25-\tfrac{1}{6}\sqrt{|A-C|}\right)

25