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

1,2

Links

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

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

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

Sequence in context: A182935 A350692 A013686 * A202147 A252417 A067918

Adjacent sequences: A153223 A153224 A153225 * A153227 A153228 A153229

Keyword

base,nonn

Author

Gil Broussard, Dec 21 2008

Extensions

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

Status

approved