A336298 Greatest prime < prime(n)/2.

2, 3, 5, 5, 7, 7, 11, 13, 13, 17, 19, 19, 23, 23, 29, 29, 31, 31, 31, 37, 41, 43, 47, 47, 47, 53, 53, 53, 61, 61, 67, 67, 73, 73, 73, 79, 83, 83, 89, 89, 89, 89, 97, 97, 103, 109, 113, 113, 113, 113, 113, 113, 127, 131, 131, 131, 137, 139, 139, 139, 151, 151

Offset: 3

Author

Clark Kimberling, Nov 16 2020

Keywords

• nonn

Comments

The n-th prime appears A102820(n) times. - Flávio V. Fernandes, Apr 08 2021

A080191 lists the distinct terms of this sequence. - Flávio V. Fernandes, Jun 19 2021

Examples

			Prime(3)/2 = 2.5, so a(3) = 2.
		

Crossrefs

Cf. A000040, A039734, A336299.

Programs

Mathematica

z = 120; t = Table[NextPrime[Prime[n]/2], {n, 3, z}]; (* A039734, A079953 *)
u = NextPrime[t, -1]  (* A336298 *)
t - u (* A336299 *)
Table[NextPrime[Prime[n]/2, -1], {n, 3, 80}] (* Wesley Ivan Hurt, Nov 26 2020 *)

PARI

a(n) = precprime(prime(n)/2); \\ Michel Marcus, Nov 16 2020

Python

from sympy import prime, prevprime
def A336298(n):
    return prevprime(prime(n)//2+1) # Chai Wah Wu, Nov 26 2020

Formula

a(n) = A151799(A000040(n)/2) for n >= 3. - Wesley Ivan Hurt, Nov 26 2020