A247747 Whole number sieve of Pi.

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, Table of n, a(n) for n = 1..552

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
def primes(n):
    """ Returns  a list of primes < n """
    sieve = [True] * n
    for i in range(3, int(n**0.5)+1, 2):
        if sieve[i]:
            sieve[i*i::2*i]=[False]*((n-i*i-1)/(2*i)+1)
    return [2] + [i for i in range(3, n, 2) if sieve[i]]
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 = 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

Cf. A000796, A245770, A258640, A258481, A257835.

Sequence in context: A357464 A249385 A347216 * A308577 A217249 A091812

Adjacent sequences: A247744 A247745 A247746 * A247748 A247749 A247750

Keyword

nonn,base

Author

Gil Broussard, Sep 23 2014

Extensions

Corrected and extended by Manfred Scheucher, Jun 05 2015

Status

approved