A385660 Numbers k such that prime(k+1)-prime(k) divides k.

1, 2, 4, 8, 10, 12, 18, 20, 24, 26, 28, 36, 44, 48, 52, 54, 60, 64, 72, 80, 84, 88, 96, 98, 102, 104, 108, 112, 116, 120, 128, 136, 140, 142, 144, 148, 152, 168, 174, 176, 178, 180, 182, 190, 192, 206, 210, 212, 216, 224, 230, 234, 236, 240, 244, 248, 252, 256, 262, 264, 268, 276, 286, 288, 294

Offset: 1

Author

Vighnesh Patil, Jul 06 2025

Keywords

• nonn
• easy

Examples

			k = 18 is a term since prime(19) - prime(18) = 6 divides 18.
		

Links

• Vighnesh Patil, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001223, A029707.

Programs

Mathematica

q[k_] := Divisible[k, Prime[k + 1] - Prime[k]]; Select[Range[300], q] (* Amiram Eldar, Jul 09 2025 *)

Python

from sympy import prime
def ok(k): return k % (prime(k+1) - prime(k)) == 0
print([k for k in range(1, 300) if ok(k)])