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A287994
Position of the first time an n-digit number appears twice in a row after the decimal point of Pi.
2
24, 413, 326, 8239, 107472, 1632152, 9719518, 106235025
OFFSET
1,1
COMMENTS
209209 and 305305 appear in Pi before any 2-digit number appears twice in a row.
EXAMPLE
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)...
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Bobby Jacobs, Sep 01 2017
EXTENSIONS
a(8) from Michael S. Branicky, Apr 24 2022
STATUS
approved