ROSECODE 399

A Big Sum

Philippe_57721 · Math · 2017-06-01

Let

S (n) = \sum_{i \leq n} (⌊ i \times \sqrt{2} ⌋) ⌊ x ⌋ = integer part of x

For instance

S (100) = 7092

What is

S (10^{20})

?

[My timing: instant]

Thanks to czp001 who gave me the idea!