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A247747
Whole number sieve of Pi.
5
1, 5, 9, 8, 4, 7, 9, 9, 5, 2, 16, 20, 62, 8, 3, 9, 28, 9, 44, 95, 58, 3, 2, 5, 8, 8, 7, 28, 0, 10, 59, 9, 7, 4, 78, 6, 6, 60, 6, 54, 66, 9, 0, 60, 9, 2, 7, 0, 1, 88, 0, 96, 9, 0, 6, 6, 0, 0, 305, 6, 4, 9, 9, 94, 270, 7, 9, 2, 6, 93, 1, 3, 5, 7, 6, 9, 35, 57, 9, 8, 0
OFFSET
1,2
LINKS
Manfred Scheucher, Sage Script
EXAMPLE
Find the first occurrence of 0 (the first whole number) in the digits of Pi (only 35 digits in this illustration):
31415926535897932384626433832795028..., and replace it with a space:
31415926535897932384626433832795 28... Repeat the process with the next whole number, 1:
3 415926535897932384626433832795 28... Then 2:
3 4159 6535897932384626433832795 28... Then 3:
4159 6535897932384626433832795 28... Then 4,5,6,7, etc., until the first occurrence of every counting number is eliminated from the digits of Pi.
1 5 9 8 4 ... Then consolidate gaps between the remaining digits into a single comma:
1,5,9,8,4,7,9,9,5,2,16,20,6,8,3,9, ... to produce the first terms in the whole number sieve of Pi.
PROG
(Python)
def arccot(x, unity):
sum = xpower = unity // x
n = 3
sign = -1
while 1:
xpower = xpower // (x*x)
term = xpower // n
if not term:
break
sum += sign * term
sign = -sign
n += 2
return sum
def pi(digits):
unity = 10**(digits + 10)
pi = 4 * (4*arccot(5, unity) - arccot(239, unity))
return pi // 10**10
a = pi(400)
b = range(100000)
y = str(a)
for x in b:
if str(x) in y:
y = y.replace(str(x), " ", 1)#replace first occurrence only
while " " in y:
y = y.replace(" ", " ")#replace long chains of spaces with a single space
z = y.split(" ")#split terms into a list
z = filter(None, z)#remove null terms
f = list(map(int, z))#convert to integers
print(f[0:-1])
# Code for A245770 by David Consiglio, Jr., Jan 03 2015
# Modified by Manfred Scheucher, Jun 05 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gil Broussard, Sep 23 2014
EXTENSIONS
Corrected and extended by Manfred Scheucher, Jun 05 2015
STATUS
approved