A109513 -id:A109513 - cp's OEIS frontend

A153228 Numbers k such that the string k is found at position 3k in the decimal digits of Pi.

1, 2, 3, 85, 200, 447263

Offset: 1

Gil Broussard, Dec 21 2008

			a(4) = 85 because 85 occurs at offset 255 (3*85) after the decimal in the digits of Pi.

Cf. A057679, A057680, A109513, A109514, A153227.

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(3*10**5+2))[:-2] # alternative to above
pi_digits = pi_digits.replace(".", "")
def afind():
    for k in range(1, len(pi_digits)):
        sk = str(k)
        if sk == pi_digits[3*k:3*k+len(sk)]:
            print(k, end=", ")
afind() # Michael S. Branicky, Jan 30 2022

a(6) corrected by Michael S. Branicky, Jan 30 2022

A153230 Numbers k such that the string k is found at position k^2 in the decimal digits of Pi.

Original entry on oeis.org

1, 3, 22, 596, 43934, 78778, 249994

Offset: 1

Gil Broussard, Dec 21 2008

a(5) > 10^4, if it exists. - Amiram Eldar, May 06 2024
From Michael S. Branicky, May 19 2025: (Start)
a(8) > 10^6.
Assuming uniformly random digits, the expected value is 0.9 terms per digit-length. (End)

			22 is in the sequence because 22 occurs at position 484 (22^2) after the decimal point in the digits of Pi.

Cf. A000796, A057679, A057680, A109513, A109514.

With[{m = 10^3}, s = Rest@ RealDigits[Pi, 10, m^2][[1]]; q[n_] := s[[n^2 + Range[0, IntegerLength[n] - 1]]] == RealDigits[n][[1]]; Select[Range[m - 1], q]] (* Amiram Eldar, May 06 2024 *)

a(5)-a(7) from Michael S. Branicky, May 18 2025

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A153228 Numbers k such that the string k is found at position 3k in the decimal digits of Pi.

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