A338521 - OEIS

%I #8 Nov 23 2020 01:46:10

%S 0,0,1,1,1,1,1,2,1,1,1,1,1,2,2,2,2,2,2,3,2,2,2,3,3,2,2,1,1,2,2,3,3,2,

%T 2,2,2,3,3,3,3,3,3,4,3,3,3,4,4,4,4,3,3,4,4,4,3,3,3,3,3,4,4,4,3,3,3,4,

%U 4,4,4,5,5,5,5,5,5,5,5,6,5,5,5,5,5,5,5

%N The number of primes between n-primepi(n) and n.

%C There is at least one prime number between n-primepi(n) and n, or a(n) >= 1, for n >= 3 (see Corollary 3 in the paper by Ya_Ping Lu attached in the links).

%H Ya-Ping Lu, <a href="/A337788/a337788.pdf">Lower Bounds for the Number of Primes in Some Integer Intervals</a>

%F a(n) = primepi(n - 1) - primepi(n - primepi(n)).

%F a(n) = A000720(n - 1) - A000720(n - A000720(n)).

%F a(n) = A000720(n -1) - A000720(A062298(n)).

%t Array[Subtract @@ Map[PrimePi, {#1 - 1, #1 - #2}] & @@ {#, PrimePi[#]} &, 105] (* _Michael De Vlieger_, Nov 05 2020 *)

%o (Python)

%o from sympy import primepi

%o for n in range(1, 101):

%o     pi = primepi(n)

%o     pi_1 = primepi(n - 1)

%o     a = pi_1 - primepi(n - pi)

%o     print(a)

%o (PARI) a(n) = primepi(n - 1) - primepi(n - primepi(n)); \\ _Michel Marcus_, Nov 01 2020

%Y Cf. A000720, A062298, A337788.

%K nonn

%O 1,8

%A _Ya-Ping Lu_, Nov 01 2020