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A153225 Numbers k such that the string k modulo 100 is found at position k in the decimal digits of Pi.

%I A153225 #10 Jan 30 2022 23:05:17
%S A153225 1,102,104,189,193,256,302,407,467,475,503,594,702,712,751,804,881,
%T A153225 905,978,998,1005,1053,1104,1107,1154,1275,1303,1306,1307,1315,1421,
%U A153225 1502,1600,1604,1690,1694,1706,1802,1860,1904,1907,1908,2006,2025,2105,2146,2208
%N A153225 Numbers k such that the string k modulo 100 is found at position k in the decimal digits of Pi.
%H A153225 Michael S. Branicky, <a href="/A153225/b153225.txt">Table of n, a(n) for n = 1..10000</a>
%e A153225 a(4) = 189 because 89 occurs at offset 189 after the decimal in the digits of Pi.
%o A153225 (Python)
%o A153225 from sympy import S
%o A153225 # download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
%o A153225 #with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()
%o A153225 pi_digits = str(S.Pi.n(3*10**5+2))[:-2] # alternative to above
%o A153225 pi_digits = pi_digits.replace(".", "")
%o A153225 def ispal(s): return s == s[::-1]
%o A153225 def agen():
%o A153225     for k in range(len(pi_digits)):
%o A153225         sk = str(k%100)
%o A153225         if sk == pi_digits[k:k+len(sk)]:
%o A153225             yield k
%o A153225 g = agen()
%o A153225 print([next(g) for n in range(1, 48)]) # _Michael S. Branicky_, Jan 30 2022
%Y A153225 Cf. A000796, A057679, A057680, A109513, A109514.
%K A153225 base,nonn
%O A153225 1,2
%A A153225 _Gil Broussard_, Dec 21 2008
%E A153225 a(47) and beyond from _Michael S. Branicky_, Jan 30 2022