2^n Digits

2^8888

Sometimes one takes on problems not for their practical purposes, but just for the sake of solving it. Since there is a limit on the number of digits that can be represented in a language like Javascript, I wanted to compute the actual output for two to a very large exponent.

One effective means of doing so is to compute 2^n and store the resulting digits in a list. The Javascript below completes this action:

var math = require('mathjs');
var log = console.log;

var sum = function(as) {
        var cc = 0;
        for(ii in as) {
                cc += as[ii];
        }
        return cc;
};

var power = function(base, k) {
        var output = [base];
        var temp = [];
        var init = 1;
        var index = 0;
        while(init < k) {
                for(ii in output) {
                        output[ii] *= 2;
                }
                if(output.length === 1 && output[0] >= 10) {
                        output.push(1);
                        output[0] = output[0] + '';
                        temp = output[0].split("")[1];
                        output[0] = Number(temp);
                }
                if(output.length === 2) {
                        if(output[0] >= 10) {
                                output[1] += 1;
                                output[0] = output[0] + '';
                                temp = output[0].split("")[1];
                                output[0] = Number(temp);
                        }
                        if(output[1] >= 10) {
                                output.push(1);
                                output[1] = output[1] + '';
                                temp = output[1].split("")[1];
                                output[1] = Number(temp);
                        }
                }
                if(output.length > 2) {
                        for(ii=0; ii <= (output.length - 2); ii++){
                                if(output[ii] >= 10) {
                                        output[ii+1] += 1;
                                        output[ii] = output[ii] + '';
                                        temp = output[ii].split("")[1];
                                        output[ii] = Number(temp);
                                }
                        }
                        index = output.length - 1;
                        if(output[index] >= 10) {
                                output[index] = output[index] + '';
                                temp = output[index].split("")[1];
                                output[index] = Number(temp);
                                output.push(1);
                        }
                }
                init += 1;
        }
        return output;
}

var agg = function(as) {
        var output = as[as.length - 1].toString();
        for(ii = (as.length - 2); ii >= 0; ii--) {
                as[ii] = as[ii].toString()
                output = output + as[ii];
        }
        return output;
};

Using this script, we can compute 2^8888 (output in image) which has a digit sum of 12055.