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

1,2

Comments

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

Links

Table of n, a(n) for n=1..19.

Formula

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

Example

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.

Prog

(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)

Crossrefs

Cf. A000796, A088143.

Cf. A014777 (if start can move).

Sequence in context: A011547 A011548 A039916 * A241217 A159500 A167834

Adjacent sequences: A378622 A378623 A378624 * A378626 A378627 A378628

Keyword

nonn,base

Author

Simon R Blow, Dec 02 2024

Status

approved