A390789 Numbers k such that 2*k - (greatest prime < 2*k) = (least prime > 2*k) - 2*k.

2, 3, 6, 9, 13, 15, 17, 21, 25, 28, 30, 32, 36, 38, 43, 51, 54, 60, 67, 69, 72, 75, 77, 80, 85, 88, 90, 93, 96, 99, 114, 118, 120, 123, 127, 130, 133, 135, 137, 141, 144, 150, 156, 162, 167, 171, 174, 178, 185, 188, 193, 207, 210, 213, 216, 218, 223, 231

Offset

1,1

Links

Table of n, a(n) for n=1..58.

Mathematica

z = 1500; f[x_] := f[x] = 2*x;
u[n_] := NextPrime[f[n], -1]; v[n_] := NextPrime[f[n]];
Select[Range[z], f[#] - v[#] < u[#] - f[#] &]   (* A390788 *)
Select[Range[z], f[#] - v[#] == u[#] - f[#] &]  (* A390789 *)
Select[Range[z], f[#] - v[#] > u[#] - f[#] &]   (* A390790 *)

Prog

(Python)
from itertools import islice
from sympy import nextprime
def A390789_gen(): # generator of terms
    p, q = 3, 5
    while True:
        a, b = divmod(p+q, 4)
        if not b:
            yield a
        p, q = q, nextprime(q)
A390789_list = list(islice(A390789_gen(), 58)) # Chai Wah Wu, Dec 01 2025

Crossrefs

Cf. A000027, A000040, A390788, A390790.

Sequence in context: A303365 A096845 A285084 * A248187 A383229 A190772

Adjacent sequences: A390786 A390787 A390788 * A390790 A390791 A390792

Keyword

nonn

Author

Clark Kimberling, Nov 25 2025

Status

approved