A287994 Position of the first time an n-digit number appears twice in a row after the decimal point of Pi.

24, 413, 326, 8239, 107472, 1632152, 9719518, 106235025

Offset: 1

Author

Bobby Jacobs, Sep 01 2017

Keywords

• nonn
• base
• more

Comments

209209 and 305305 appear in Pi before any 2-digit number appears twice in a row.

Examples

			a(1) = 24 because the first time a 1-digit number appears twice in a row in the decimal expansion of Pi is 24 digits after the decimal point: 3.14159265358979323846264(33)...
		

Crossrefs

Cf. A000796, A288291, A290977.

Programs

Mathematica

s = First@ RealDigits[Pi,10,10^7]; Table[p = Partition[s,k,1];
SelectFirst[ Range[ Length[p] - k], p[[#]] == p[[# + k]] &] - 1, {k, 7}] (* Giovanni Resta, Sep 05 2017 *)

Python

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(2*10**5))[:-1] # alternative to above
pi_digits = pi_digits.replace(".", "")
def a(n):
    idx = 1
    while pi_digits[idx:idx+n] != pi_digits[idx+n:idx+2*n]:
        idx += 1
        assert idx + 2*n < len(pi_digits), "increase precision"
    return idx
print([a(n) for n in range(1, 6)]) # Michael S. Branicky, Apr 24 2022

Extensions

a(8) from Michael S. Branicky, Apr 24 2022