A380877 - OEIS

%I #10 Mar 03 2025 10:47:28

%S 2,3,5,13,17,433,457,461

%N Primes p where the prime race 12m+1 versus 12m+7 is tied.

%C Primes p such that pi_{12,1}(p) = pi_{12,7}(p), where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m). For the first 5 billion primes, pi_{12,7}(p) >= pi_{12,1}(p). If exists, a(9) > 122430513841.

%t s={};Do[p=Prime[pp];If[Length[Select[Prime[Range[pp]],Mod[#,12]==1&]]==Length[Select[Prime[Range[pp]],Mod[#,12]==7&]],AppendTo[s,p]],{pp,100}];s (* _James C. McMahon_, Mar 03 2025 *)

%o (Python)

%o from sympy import nextprime; p, d = 2, 0

%o while p < 500:

%o     if d == 0: print(p, end = ', ')

%o     p = nextprime(p); r = p%12

%o     if r == 7: d += 1

%o     elif r == 1: d -= 1

%Y Cf. A007351, A068228, A068229, A379989, A380333.

%K nonn,new

%O 1,1

%A _Ya-Ping Lu_, Feb 06 2025