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calculation of sum of 2^(f(n))

Source: Indonesia IMO 2010 TST, Stage 1, Test 2, Problem 4

November 12, 2009
combinatorics proposedcombinatorics

Problem Statement

For each positive integer n n, define f(n) f(n) as the number of digits 0 0 in its decimal representation. For example, f(2)\equal{}0, f(2009)\equal{}2, etc. Please, calculate S\equal{}\sum_{k\equal{}1}^{n}2^{f(k)}, for n\equal{}9,999,999,999. Yudi Satria, Jakarta
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