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A153226
Numbers k such that the string k modulo 1000 is found at position k in the decimal digits of Pi.
1
1, 1005, 1053, 1255, 2006, 2025, 2246, 2560, 3712, 4063, 4066, 4087, 5006, 5009, 5038, 5068, 5076, 5538, 6000, 6025, 6045, 7007, 7025, 7037, 8068, 8960, 9009, 9052, 10007, 10823, 11003, 11005, 12000, 12003, 12134, 12639, 14009, 14207, 14326, 14944, 15052, 16000
OFFSET
1,2
LINKS
EXAMPLE
a(4) = 1255 because 255 occurs at offset 1255 after the decimal in the digits of Pi.
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(3*10**5+2))[:-2] # alternative to above
pi_digits = pi_digits.replace(".", "")
def ispal(s): return s == s[::-1]
def agen():
for k in range(len(pi_digits)):
sk = str(k%1000)
if sk == pi_digits[k:k+len(sk)]:
yield k
g = agen()
print([next(g) for n in range(1, 43)]) # Michael S. Branicky, Jan 30 2022
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Gil Broussard, Dec 21 2008
EXTENSIONS
a(40) and beyond from Michael S. Branicky, Jan 30 2022
STATUS
approved