Tried to brute force a tricky real sequence. termux on redmi 4 hangs on (yoo 5). lol

a-tricky-real-sequence.scm

(define (yoo n)
  (cond
    ( (= n 0) (intxdx 0 1))
    ( ( = n 1) (intxdx (intxdx 0 (/ 1 2)) (intxdx (/ 1 2) 1)))
    ( else
  (let
    ((N (expt 2 n)))
    (intxdx
      (calcdown N (/ N 2))
      (calcup N (/ N 2)))))))

(define (intxdx low up)
  ;; (display "yo\n")
  (exact->inexact (/ (* (+ low up) (- up low)) 2)))

(define (calcup pow2n i)
  (if (= (+ 1 i) pow2n)
    (intxdx (/ i pow2n) 1)
    (intxdx
      (/ i pow2n)
      (intxdx
	(/ (+ i 1) pow2n)
	(calcup pow2n (+ i 1))))))

(define (calcdown pow2n i)
  (if (= i 1)
    (intxdx 0 (/ 1 pow2n))
    (intxdx
      (intxdx
	(calcdown pow2n (- i 1))
	(/ (- i 1) pow2n))
      (/ i pow2n))))

(define (ell n) (/ (log (/ 0.25 (abs (yoo n)))) (log 2)))

(define (lim n) (- (ell n) (+ 4 n)))

a_tricky_real_sequence.c

#include <stdio.h>
#include <math.h>
#include <stdlib.h>


double intxdx(double low, double up) {
    	return (low+up)*(up-low)/2;
}

double calcup(unsigned n) {
    double POW2N = pow(2.0, n);
    double i = POW2N;
    double up = 1.0;
    double down;
    while (i > 1 + POW2N/2) {
        down = (i-1.0)/POW2N;
        up = intxdx(down, up);
        up = intxdx(down, up);
        i = i - 1;
    }
    down = 0.5;
    up = intxdx(down, up);
    return up;
}

double calcdown(unsigned n) {
    double POW2N = pow(2.0, n);
    double i = 0;
    double down = 0.0;
    double up;
    while (i + 1 < POW2N/2) {
        up = (i+1.0)/POW2N;
        down = intxdx(down, up);
        down = intxdx(down, up);
        i = i + 1;
    }
    up = 0.5;
    down = intxdx(down, up);
    return down;
}

double yoo(unsigned n) {
	switch(n) {
		case 0: return intxdx(0, 1);
		case 1: return intxdx(intxdx(0, 0.5), intxdx(0.5, 1));
		default: return intxdx(calcdown(n), calcup(n));
	}
}

double ell(unsigned n) {
	return log(0.25/fabs(yoo(n)))/log(2);
}


int main(int argc, char **argv) {
	int n = 0, i = 0;
	if (argc > 1) {
		n = atoi(argv[1]);
	}
    if (n == 0) {
        n = 21;
    }
    for (i = 0; i <= n; i++ ) {
        printf( "%4d\t%4.16f\n", i, ell(i) );
    }
    return 0;
}

/*
compile using: `cc a_tricky_real_sequence.c -o trickyseq -lm`
run using: `./trickyseq 30`
*/

a_tricky_real_sequence.py

import math

def yoo(n):
    if n == 0:
        return intxdx(0,1)
    elif n == 1:
        return intxdx(intxdx(0, 0.5), intxdx(0.5, 1))
    else:
        return intxdx(calcdown(n), calcup(n))

def intxdx(low, up):
    return (low+up)*(up-low)/2.0

def calcup(n):
    POW2N = 2.0**n
    i = POW2N
    up = 1.0
    while i > 1 + POW2N/2:
        down = (i-1.0)/POW2N
        up = intxdx(down, up)
        up = intxdx(down, up)
        i = i - 1
    down = 0.5
    up = intxdx(down, up)
    return up

def calcdown(n):
    POW2N = 2.0**n
    i = 0
    down = 0.0
    while i < POW2N/2 -1:
        up = (i+1.0)/POW2N
        down = intxdx(down, up)
        down = intxdx(down, up)
        i = i + 1
    up = 0.5
    down = intxdx(down, up)
    return down

def ell(n):
    return math.log2(1.0/(4*abs(yoo(n))))

if __name__ == '__main__':
    for i in range(21):
        print(i, ell(i))