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

%I A383502 #18 May 30 2025 00:49:35
%S A383502 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,
%T A383502 191,12,127,52,3,36,275,88,589,283,40,290,952,47,10,1213,750,572,84,
%U A383502 126,2,282,162,125,480,26,66,185,157,1490,1310,832,1321,352
%N A383502 Position of the first instance of prime(n), in base 3, in the ternary representation of Pi after the ternary point.
%C A383502 Positions are numbered starting from 1 for the first ternary digit after the ternary point in Pi.
%e A383502 The ternary digits of Pi and their numbering, after the ternary point, begin
%e A383502           1 2 3 4 5 6 7 8 9 ...
%e A383502    0 1  . 0 2 1 1 0 1 2 2 2 2 0 1 0 2 ...
%e A383502                     \---/
%e A383502 prime(7) is 17, or 122_3, which first appears at position 6.
%o A383502 (Python)
%o A383502 import gmpy2
%o A383502 from sympy import isprime
%o A383502 def to_base3(n):
%o A383502     if n == 0: return '0'
%o A383502     d = []
%o A383502     while n: d.append(str(n % 3)); n //= 3
%o A383502     return ''.join(reversed(d))
%o A383502 gmpy2.get_context().precision = 1200000
%o A383502 pi_ternary = gmpy2.digits(gmpy2.const_pi(),3)[0][4:]  # skip "10."
%o A383502 out = []
%o A383502 for p in range(2, 280):
%o A383502     if isprime(p):
%o A383502         pos = pi_ternary.find(to_base3(p)) + 1
%o A383502         out.append(pos)
%o A383502 print(out)
%Y A383502 Cf. A000040, A178707, A007089, A004602, A004601.
%K A383502 base,nonn
%O A383502 1,1
%A A383502 _James S. DeArmon_, Apr 28 2025