i solved a problem featured on the yc company interviewstreet.com codesprint.

the problem: Count the number of one-bits from 0 to 2^n - 1, for n from 1 to 20.

my solution: http://i.imgur.com/hUxt0.png

when you run the solution:

     Number of one-bits in 1 bit numbers from 0 to 1 = 1
     Number of one-bits in 2 bit numbers from 0 to 3 = 4
     Number of one-bits in 3 bit numbers from 0 to 7 = 12
     Number of one-bits in 4 bit numbers from 0 to 15 = 32
     Number of one-bits in 5 bit numbers from 0 to 31 = 80
     Number of one-bits in 6 bit numbers from 0 to 63 = 192
     Number of one-bits in 7 bit numbers from 0 to 127 = 448
     ....

JS:

    var list;
    var x;
    var prev;
    var onebits;
    var doubleatprev;

    list = [];
    list[0] = 1;
    list[1] = 4;
    for (x = 2; x <= 20; x++) {
    prev = x;
    onebits = Math.pow(2, prev);
    doubleatprev = list[x - 1] * 2;
    list[1 + x - 1] = onebits + doubleatprev;
    }
    for (x = 1; x <= 20; x++) {
      window.alert(['Number of one-bits in ',x,' bit numbers    from 0 to ',Math.pow(2, x) - 1,' = ',list[x - 1]].join(''));
    }

Took 15 minutes to code up and 45 minutes to debug the array indexing :) One of these days I'll be able to write the JS and get the Blockly instead of the other way around - that'd be super awesome!