How do you share files here? You can't. I have the one-page proof in PDF format. But I'm not 100% sure it's the proof I used two years ago. Infact, I don't know what I was thinking two years ago.

I forgot. Now I can't sleep until I know the answer. It's 20:50, Nice. Give me five minutes, I read this on my phone.

Your results:

// sumDigPow(1L, 50000000L) => 21 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz
// sumDigPow(1L, 100000000L) => 41 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz
// sumDigPow(1L, 200000000L) => 94 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz
// sumDigPow(1L, 500000000L) => ?? seconds on Intel(R) Core(TM) i3-3120M 2.50GHz

My results:

// sumDigPow(1L, 50000000L) => 7 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz
// sumDigPow(1L, 100000000L) => 14 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz
// sumDigPow(1L, 200000000L) => 30 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz
// sumDigPow(1L, 500000000L) => 80 seconds on Intel(R) Core(TM) i3-3120M 2.50GHz

@MuaazK - that sounds like a good idea. I forked a solution using your suggestion.

If the array's length is 10,000,000 and there are only 5 odd numbers in the first 10 positions, the 'for' loop will put them back in their places and continue to scan the array for no reason.
you should check: "s < sortedOdd.length" and break when it is false.