#OK to post homework
#George Spahn, 3-13-2022, Assignment 15

#1

DecDigits := proc(a,K) 
local left, a1, k, t, L:
  left := floor(log(a)/log(10))+1:
  a1:=a:
  for k from 1 to K do
    t := 10^(left-k):
	L[k] := floor(a1/t):
	a1 := a1 - L[k]*t:
  od:
  
  [seq(L[i],i = 1.. K)]:
  
end:


#6

# starting at around N=400, PiAp(N) takes more than 5 seconds.
# PiApc(N) can get up to N = 1500 in under 5 seconds.

# This makes sense because the recurrence should be much faster than computing the integral.


#7
Jesus := proc(n)
  t1 := 0:
  f := 1:
  p := 1:
  for k from 1 to n do
    f := -1 * f * (2 * k - 1) / (2 * k):
    p := p * 2^10:
    top := 20 * k * (50 + 41 * (k - 1)) + 13:
    t1 := t1 + (f)^5 * top / p:
  od:

  t1 := t1 + 13:
  (128 / t1)^.5:
end:

# The error in Jesus(20) is about 10^-9