|
|
A338521
|
|
The number of primes between n-primepi(n) and n.
|
|
1
|
|
|
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, 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, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
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).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = primepi(n - 1) - primepi(n - primepi(n)).
|
|
MATHEMATICA
|
Array[Subtract @@ Map[PrimePi, {#1 - 1, #1 - #2}] & @@ {#, PrimePi[#]} &, 105] (* Michael De Vlieger, Nov 05 2020 *)
|
|
PROG
|
(Python)
from sympy import primepi
for n in range(1, 101):
pi = primepi(n)
pi_1 = primepi(n - 1)
a = pi_1 - primepi(n - pi)
print(a)
(PARI) a(n) = primepi(n - 1) - primepi(n - primepi(n)); \\ Michel Marcus, Nov 01 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|