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
Examples
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.
Links
- Manfred Scheucher, Table of n, a(n) for n = 1..552
- Manfred Scheucher, Sage Script
Programs
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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 = 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
Extensions
Corrected and extended by Manfred Scheucher, Jun 05 2015
Comments