A038100 Numbers k such that k < first location of string of k in decimal expansion of Pi.

0, 2, 3, 6, 7, 8, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 34, 36, 37, 39, 40, 42, 44, 45, 47, 48, 49, 52, 54, 55, 56, 57, 60, 61, 63, 66, 67, 68, 70, 72, 73, 76, 77, 80, 85, 87, 90, 91, 96, 100, 101, 102, 103, 104, 106, 107, 108

Offset: 1

Author

Patrick De Geest, Feb 15 1999

Keywords

• nonn
• base

Comments

'Location' starts from the first digit after the decimal point and refers to the first digit of a(n).

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..5000
• Dave Andersen, The Pi-Search Page

Crossrefs

Cf. A000796, A014777, A038099.

Programs

Python

from sympy import pi
from itertools import count, islice
digits_of_pi = str(pi.n(10**5))[1:-1]
def agen():
    for k in count(0):
        kloc = digits_of_pi.find(str(k))
        assert kloc > 0, ("Increase precision", k)
        if k < kloc: yield k
print(list(islice(agen(), 65))) # Michael S. Branicky, Jul 10 2022

Formula

a(n) < A014777(n). - Michael S. Branicky, Jul 10 2022

Extensions

Offset changed to 1 by Jinyuan Wang, Sep 04 2021