A153226 Numbers k such that the string k modulo 1000 is found at position k in the decimal digits of Pi.

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

Author

Gil Broussard, Dec 21 2008

Keywords

• base
• nonn

Examples

			a(4) = 1255 because 255 occurs at offset 1255 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%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

Extensions

a(40) and beyond from Michael S. Branicky, Jan 30 2022