A390788 Numbers k such that 2*k - (greatest prime < 2*k) < (least prime > 2*k) - 2*k.

4, 7, 10, 12, 16, 19, 22, 24, 27, 31, 34, 37, 40, 42, 45, 46, 49, 52, 55, 57, 58, 59, 64, 66, 70, 71, 76, 79, 82, 84, 87, 91, 92, 97, 100, 101, 102, 106, 107, 108, 112, 115, 117, 121, 122, 126, 129, 132, 136, 139, 142, 143, 147, 148, 149, 154, 157, 159, 160

Offset

1,1

Comments

Let (f(k)) be an increasing sequence of positive composite numbers. Let u(k) = greatest prime < f(k) and v(k) = least prime > f(k). Let

s(1) = {k : f(k) - u(k) < v(k) - f(k)} = {k : f(k) < (u(k)+v(k))/2};

s(2) = {k : f(k) - u(k) = v(k) - f(k)} = {k : f(k) = (u(k)+v(k))/2};

s(3) = {k : f(k) - u(k) > v(k) - f(k)} = {k : f(k) > (u(k)+v(k))/2}.

Guide to related sequences:

f(k) = 2*k: A390788, A390789, A390790

f(k) = 3*k: A391351, A391352, A391353

f(k) = 4*k: A391354, A391355, A391356

f(k) = 5*k: A392110, A392111, A392112

f(k) = 6*k: A392113, A392114, A392115

f(k) = k^2: A109269, A075190, A109270 (if 1 is included)

f(k) = k^3: A392120, A075191, A392122

f(k) = k*(k+1)/2: A392123, A181902, A392125

Links

Table of n, a(n) for n=1..59.

Example

2*4 - 7 < 11 - 2*4, so 4 is in the list.

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 *)

Crossrefs

Cf. A000027, A000040, A390789, A390790.

Sequence in context: A080734 A310676 A320929 * A104280 A083032 A284933

Adjacent sequences: A390785 A390786 A390787 * A390789 A390790 A390791

Keyword

nonn

Author

Clark Kimberling, Nov 25 2025

Status

approved