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

1,1

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?

Links

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

Example

Pi = 3.141592653589...

Prog

(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

Crossrefs

Cf. A000796.

Sequence in context: A095328 A375854 A066712 * A058361 A112668 A016734

Adjacent sequences: A064806 A064807 A064808 * A064810 A064811 A064812

Keyword

base,nonn,look

Author

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

Status

approved