A356466 - OEIS

%I #10 Apr 25 2024 13:53:45

%S 11,13,17,19,29,31,59,61,79,83,127,131,137,139,149,151,163,167,179,

%T 181,191,193,197,199,239,241,331,337,347,349,397,401,419,421,431,433,

%U 439,443,521,523,541,547,673,677,701,709,787,797,809,811,821,823,827,829

%N Prime numbers in the sublists defined in A348168 that contain exactly two primes.

%C Let g = q - p be the gap between a pair of primes in the sequence, g < p - previprime(p) and g < nextprime(q) - q.

%C It seems that lim_{n-> oo} n/primepi(a(n)) = 0.314 approximately.

%o (Python)

%o from sympy import nextprime; R = []; p0 = 2

%o while len(R) < 60:

%o     p1 = nextprime(p0); M = [p1]; p = nextprime(p1); g1 = p - p1

%o     while g1 < p1 - p0 and p - p1 <= g1: M.append(p); p1 = p; p = nextprime(p)

%o     if len(M) == 2: R.extend(M)

%o     p0 = p1

%o print(*R, sep = ', ')

%Y Cf. A348168.

%K nonn

%O 1,1

%A _Ya-Ping Lu_, Aug 08 2022