Loïc Grenié on Sun, 22 Jan 2023 16:44:10 +0100

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Re: Computing integer sequences via integrals

On Sat Jan. 21st, 2023, at 18:00, Georgi Guninski wrote:
Many thanks for the answer.

Is there simple "primitive" for computing \int 2^2^floor(x) dx?

    It's not clear what you want to integrate: 2^floor(x)? In that case,
  I think

(x-floor(x))*2^floor(x) + 2^(floor(x)+1)-1

  should be equal to

\int_0^x 2^floor(t) dt.

You write jumps cause problems.
A lot of builtin functions have jumps, e.g. tan().
Are (definite) integrals with tan() problem?

     Definitely if you include a jump: the integral is not convergent. Otherwise,
   everything is fine (and you do not see the jumps).