A378625 The first subsequence starting at the first digit after the decimal point in the decimal expansion of Pi that is divisible by n.

1, 14, 141, 141592, 1415, 141592653589793238, 14, 141592, 141592653, 14159265358979323846264338327950, 141592, 1415926535897932384626433832795028, 14159265358979, 14, 14159265, 1415926535897932384, 141592653589793, 141592653589793238, 141592653589793238462

Offset: 1

Author

Simon R Blow, Dec 02 2024

Keywords

• nonn
• base

Comments

For every positive integer n there exists a contiguous subsequence of the decimal expansion of Pi that is divisible by n (conjectured).

Examples

			a(3) = 141 is the first integer in the sequence that is divisible by 3.
a(6) = 141592653589793238 is the first integer in the sequence that is divisibe by 6.
		

Crossrefs

Cf. A000796, A088143.

Cf. A014777 (if start can move).

Programs

Python

from mpmath import mp
mp.dps = 1000000
pi_digits = str(mp.pi)[2:]
def first_divisible(n):
    current_number = 0
    for digit in pi_digits:
        current_number = current_number * 10 + int(digit)
        if current_number % n == 0:
            return current_number
    return None
results = [first_divisible(n) for n in range(1, 21)]
print(results)

Formula

a(n) = n * A088143(n). - Alois P. Heinz, Dec 05 2024