OFFSET
1,1
COMMENTS
Conjecture: 1323 is the final term.
If there are at least as many primes in [1, m] as there are in [m+1, 2*m] for all positive integers m, then this sequence consists of the numbers k such that A342068(k)=3.
EXAMPLE
The intervals [1, 100], [101, 200], and [201, 300] contain 25, 21, and 16 primes respectively (cf. A038822); 16 < 21, so 100 is not a term of the sequence.
The intervals [1, 20], [21, 40], and [41, 60] contain 8, 4, and 5 primes, respectively; 5 > 4, so 20 is a term.
PROG
(Python)
from sympy import primepi
def ok(n): return primepi(3*n) > 2*primepi(2*n) - primepi(n)
print([m for m in range(9999) if ok(m)]) # Michael S. Branicky, Mar 23 2021
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jon E. Schoenfield, Mar 23 2021
STATUS
approved