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First Digit of 4

Source: ToT - 2001 Fall Junior A-Level #7

August 17, 2011
number theory unsolvednumber theory

Problem Statement

It is given that 23332^{333} is a 101-digit number whose first digit is 1. How many of the numbers 2k2^k, 1≤k≤3321\le k\le 332 have first digit 4?
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