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A153227 Numbers k such that the string k is found at position 2k in the decimal digits of Pi.

%I A153227 #13 Jan 30 2022 15:58:57
%S A153227 5,95,171,529,1913,2753,60597,831092,9552919
%N A153227 Numbers k such that the string k is found at position 2k in the decimal digits of Pi.
%e A153227 a(2) = 95 because 95 occurs at offset 190 (2*95) after the decimal in the digits of Pi.
%o A153227 (Python)
%o A153227 from sympy import S
%o A153227 # download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
%o A153227 #with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()
%o A153227 pi_digits = str(S.Pi.n(3*10**5+2))[:-2] # alternative to above
%o A153227 pi_digits = pi_digits.replace(".", "")
%o A153227 def afind():
%o A153227     for k in range(1, len(pi_digits)):
%o A153227         sk = str(k)
%o A153227         if sk == pi_digits[2*k:2*k+len(sk)]:
%o A153227             print(k, end=", ")
%o A153227 afind() # _Michael S. Branicky_, Jan 30 2022
%Y A153227 Cf. A057679, A057680, A109513, A109514, A153228.
%K A153227 base,more,nonn
%O A153227 1,1
%A A153227 _Gil Broussard_, Dec 21 2008
%E A153227 a(8) corrected by _Paul Tek_, Jun 09 2013
%E A153227 a(9) from _Michael S. Branicky_, Jan 30 2022