A245770 Prime sieve of Pi.

1, 9, 6, 5, 93, 84626, 3, 2, 502884, 69399, 5105820, 4944, 2, 816406286, 986, 4825342, 70, 9, 480865, 2, 66, 93, 55058, 25, 4081284, 174, 270, 85, 555964462, 4895, 9644288, 7566, 344, 28475648, 8, 65, 201, 45648, 23, 4543, 393, 2602, 412, 724, 660, 55, 74881, 20962, 25, 1715364, 892, 600

Offset

1,2

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1029 (first 422 terms from Manfred Scheucher)

Manfred Scheucher, Sage Script (Note: should also run in pure python with a few modifications)

Example

Find the first occurrence of prime 2 in the digits of Pi (only 25 digits in this illustration):
3141592653589793238462643..., and replace it with a space:
314159 653589793238462643...  Repeat the process with 3:
14159 653589793238462643...  Then 5:
141 9 653589793238462643...  Then 7:
141 9 653589 93238462643...  Then 11, 13, 17, etc., until the first occurrence of every prime is eliminated from the digits of Pi.
1   9 6  5   93  84626  ...  Then consolidate gaps between the remaining digits into a single comma:
1,9,6,5,93,84626,...         to produce the first terms in the prime 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(370)
b = primes(100000000)
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])
# David Consiglio, Jr., Jan 03 2015

Crossrefs

Cf. A000796, A246022, A248804 (Prime sieve of e), A248831 (Prime sieve of sqrt(2)).

Sequence in context: A144665 A019884 A103814 * A117020 A011459 A354295

Adjacent sequences: A245767 A245768 A245769 * A245771 A245772 A245773

Keyword

nonn,base

Author

Gil Broussard, Aug 01 2014

Extensions

a(14) corrected by Manfred Scheucher, May 25 2015

Status

approved