[VA] Short & Sweet Math Challenge #24: "2019 Spring Special 5-tier"

[Albert Chan]

(04-02-2019 10:43 PM)Valentin Albillo Wrote:       
       >RUN
              20    3.40706916561     { it converged to the limit after fitting the first 20 primes: 2, 3, 5, ..., 71) }

I think you meant sum converged using 19 primes (20 primes to confirm 12-digits convergence)

sum using 19 primes = 414453 270752 384363 / 19! ≈ 3.40706 916563
sum using 20 primes = 414453 270752 580132 / 19! ≈ 3.40706 916563

Also, forward difference tables may be built incrementally.

C(1) = p1
C(2) = p2 - p1
C(3) = p3 - 2 p2 + p1,
C(4) = p4 - 3 p3 + 3 p2 - p1,
C(5) = p5 - 4 p4 + 6 p3 - 4 p2 + p1,
...

Above can be simplified without a prime table:

C(1) = p1
C(2) = p2 - C(1)
C(3) = p3 - C(1) - 2 C(2)
C(4) = p4 - C(1) - 3 C(2) - 3 C(3)
C(5) = p5 - C(1) - 4 C(2) - 6 C(3) - 4 C(4)
...