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Prime numbers in the sublists defined in A348168 that contain a single prime.
1

%I #20 Apr 25 2024 13:53:31

%S 2,3,5,7,23,53,89,157,173,211,293,353,359,409,449,683,691,839,919,977,

%T 983,1039,1069,1103,1109,1201,1223,1237,1283,1327,1381,1439,1459,1511,

%U 1613,1627,1637,1709,2039,2099,2179,2213,2221,2243,2251,2273,2447,2633,2917

%N Prime numbers in the sublists defined in A348168 that contain a single prime.

%C It seems that lim_{n->oo} n/primepi(a(n)) = 0.102 approximately.

%o (Python)

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

%o while len(R) < 50:

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

%o if g1 >= p1 - p0: R.append(p1)

%o else:

%o while p - p1 <= g1: p1 = p; p = nextprime(p)

%o p0 = p1

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

%Y Cf. A348168.

%K nonn

%O 1,1

%A _Ya-Ping Lu_, Aug 01 2022