A234962 Primes missing from the tree generated at A234960.

71, 101, 109, 151, 181, 191, 229, 233, 239, 241, 269, 283, 311, 349, 367, 373, 379, 409, 419, 433, 439, 461, 463, 467, 479, 487, 491, 569, 571, 593, 599, 601, 607, 643, 647, 653, 659, 683, 727, 733, 739, 743, 751, 757, 811, 821, 823, 827, 829, 857, 877, 881

Offset

1,1

Comments

According to the conjecture at A234961, the limiting relative density of these primes is 1.

Links

Clark Kimberling, Table of n, a(n) for n = 1..7000

Mathematica

t = NestList[DeleteDuplicates[Flatten[Map[{#, NextPrime[2 #, -1], NextPrime[2 #, 1]} &, #]]] &, {2}, 12]; Complement[Map[Prime, Range[PrimePi[Last[#]]]], #] &[Last[t]] (* Peter J. C. Moses, Dec 30 2013 *)

Prog

(Python)
from sympy import prevprime, nextprime, primerange
def aupto(limit):
    reach, expand = {2}, [2]
    while True:
        newreach = set()
        while len(expand) > 0:
            p = expand.pop()
            for q in prevprime(2*p), nextprime(2*p):
                if q not in reach:
                    newreach.add(q)
        reach |= newreach
        expand = list(newreach)
        if prevprime(2*min(expand)) > limit:
            in_tree = set(r for r in reach if r <= limit)
            return sorted(set(primerange(1, limit+1)) - in_tree)
print(aupto(881)) # Michael S. Branicky, Jul 24 2022

Crossrefs

Cf. A234960, A234961.

Sequence in context: A155953 A247200 A288907 * A166252 A339466 A339463

Adjacent sequences: A234959 A234960 A234961 * A234963 A234964 A234965

Keyword

nonn

Author

Clark Kimberling, Jan 01 2014

Status

approved