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
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)...
Programs
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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
Comments