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A356466
Prime numbers in the sublists defined in A348168 that contain exactly two primes.
0
11, 13, 17, 19, 29, 31, 59, 61, 79, 83, 127, 131, 137, 139, 149, 151, 163, 167, 179, 181, 191, 193, 197, 199, 239, 241, 331, 337, 347, 349, 397, 401, 419, 421, 431, 433, 439, 443, 521, 523, 541, 547, 673, 677, 701, 709, 787, 797, 809, 811, 821, 823, 827, 829
OFFSET
1,1
COMMENTS
Let g = q - p be the gap between a pair of primes in the sequence, g < p - previprime(p) and g < nextprime(q) - q.
It seems that lim_{n-> oo} n/primepi(a(n)) = 0.314 approximately.
PROG
(Python)
from sympy import nextprime; R = []; p0 = 2
while len(R) < 60:
p1 = nextprime(p0); M = [p1]; p = nextprime(p1); g1 = p - p1
while g1 < p1 - p0 and p - p1 <= g1: M.append(p); p1 = p; p = nextprime(p)
if len(M) == 2: R.extend(M)
p0 = p1
print(*R, sep = ', ')
CROSSREFS
Cf. A348168.
Sequence in context: A132247 A186811 A038926 * A168446 A275467 A376303
KEYWORD
nonn
AUTHOR
Ya-Ping Lu, Aug 08 2022
STATUS
approved