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

1, 102, 104, 189, 193, 256, 302, 407, 467, 475, 503, 594, 702, 712, 751, 804, 881, 905, 978, 998, 1005, 1053, 1104, 1107, 1154, 1275, 1303, 1306, 1307, 1315, 1421, 1502, 1600, 1604, 1690, 1694, 1706, 1802, 1860, 1904, 1907, 1908, 2006, 2025, 2105, 2146, 2208

Offset: 1

Author

Gil Broussard, Dec 21 2008

Keywords

• base
• nonn

Examples

			a(4) = 189 because 89 occurs at offset 189 after the decimal in the digits of Pi.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000796, A057679, A057680, A109513, A109514.

Programs

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%100)
        if sk == pi_digits[k:k+len(sk)]:
            yield k
g = agen()
print([next(g) for n in range(1, 48)]) # Michael S. Branicky, Jan 30 2022

Extensions

a(47) and beyond from Michael S. Branicky, Jan 30 2022