Question

How to find the first power of 2 whose leading digits are 12 in C

Answer 1

#include <stdio.h>
#include <math.h>
#include <string.h>

// return 1 if 2^n starts with prefix, else 0 
int startsWithPrefix(long long n, int prefix) {
    static const double log2v = log10(2.0);

    double x = n * log2v;
    double frac = x - floor(x);

    // count digits in prefix 
    char buf[32] = "";
    sprintf(buf, "%d", prefix);
    int digits = strlen(buf);

    // compute leading digits 
    int leading = (int) pow(10, frac + digits - 1);

    return leading == prefix;
}

int main(void) {
    int prefix = 12;

    for (long long n = 1; ; n++) {
        if (startsWithPrefix(n, prefix)) {
            printf("First n = %lld\n", n);
            printf("2 ^ %lld = %d\n", n, (int) pow(2, n)); 
            break;
        }
    }
}


/*
run:

First n = 7
2 ^ 7 = 128

*/

 

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