A064809 Decimal expansion of Pi written as a sequence of positive integers avoiding duplicates.

3, 1, 4, 15, 9, 2, 6, 5, 35, 8, 97, 93, 23, 84, 62, 64, 33, 83, 27, 950, 28, 841, 971, 69, 39, 937, 510, 58, 20, 974, 94, 45, 92, 30, 7, 81, 640, 628, 620, 89, 98, 6280, 34, 82, 53, 42, 11, 70, 67, 982, 14, 80, 86, 51, 32, 8230, 66, 470, 938, 44, 60, 95, 50, 582, 231, 72

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Oct 22 2001

Keywords

• base
• nonn
• look

Comments

Start with the first digit of Pi and set a(1)=3. Let p(1),...,p(i) be the digits of Pi used to construct a(1),...,a(n); then a(n+1) is the smallest integer with digits p(i+1),...,p(i+j) such that a(n+1) is new and p(i+j+1) != 0.

Is the sequence a permutation of the positive integers?

Examples

			Pi = 3.141592653589...
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000796.

Programs

Python

from itertools import islice
from sympy import S
# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
# with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()
pi_digits = str(S.Pi.n(10**5))[:-1] # alternative to above
pi_digits = pi_digits.replace(".", "")
def diggen(): yield from map(int, pi_digits)
def agen(): # generator of terms
    g = diggen()
    aset, nextd = set(), next(g)
    while True:
        an, nextd = nextd, next(g)
        while an in aset or nextd == 0:
            an, nextd = int(str(an) + str(nextd)), next(g)
        yield an
        aset.add(an)
print(list(islice(agen(), 66))) # Michael S. Branicky, Mar 31 2022