A356466 - OEIS

A356466

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

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

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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.

LINKS

Table of n, a(n) for n=1..54.

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

Adjacent sequences: A356463 A356464 A356465 * A356467 A356468 A356469

KEYWORD

nonn

AUTHOR

Ya-Ping Lu, Aug 08 2022

STATUS

approved