A383502 Position of the first instance of prime(n), in base 3, in the ternary representation of Pi after the ternary point.

2, 4, 6, 2, 12, 20, 6, 10, 27, 16, 85, 3, 35, 78, 95, 6, 38, 96, 19, 27, 9, 66, 157, 171, 81, 191, 12, 127, 52, 3, 36, 275, 88, 589, 283, 40, 290, 952, 47, 10, 1213, 750, 572, 84, 126, 2, 282, 162, 125, 480, 26, 66, 185, 157, 1490, 1310, 832, 1321, 352

Offset: 1

Author

James S. DeArmon, Apr 28 2025

Keywords

• base
• nonn

Comments

Positions are numbered starting from 1 for the first ternary digit after the ternary point in Pi.

Examples

			The ternary digits of Pi and their numbering, after the ternary point, begin
          1 2 3 4 5 6 7 8 9 ...
   0 1  . 0 2 1 1 0 1 2 2 2 2 0 1 0 2 ...
                    \---/
prime(7) is 17, or 122_3, which first appears at position 6.
		

Crossrefs

Cf. A000040, A178707, A007089, A004602, A004601.

Programs

Python

import gmpy2
from sympy import isprime
def to_base3(n):
    if n == 0: return '0'
    d = []
    while n: d.append(str(n % 3)); n //= 3
    return ''.join(reversed(d))
gmpy2.get_context().precision = 1200000
pi_ternary = gmpy2.digits(gmpy2.const_pi(),3)[0][4:]  # skip "10."
out = []
for p in range(2, 280):
    if isprime(p):
        pos = pi_ternary.find(to_base3(p)) + 1
        out.append(pos)
print(out)