A217721 Number of primes between n^2 - log_2(n)^2 and n^2 (inclusive).

0, 1, 1, 1, 1, 1, 2, 2, 3, 2, 1, 2, 3, 2, 2, 2, 3, 4, 4, 3, 3, 2, 3, 4, 4, 3, 3, 3, 5, 4, 4, 4, 2, 2, 4, 5, 2, 5, 2, 3, 4, 4, 3, 4, 5, 5, 3, 5, 7, 2, 3, 6, 6, 4, 5, 3, 3, 5, 6, 4, 5, 3, 3, 4, 4, 4, 4, 4, 4, 3, 5, 5, 4, 4, 2, 4, 4, 5, 5, 6, 5, 6, 5, 4, 6, 2, 7

Offset

1,7

Comments

Conjecture: a(n) > 0 for n > 1.

Conjecture checked up to n = 2^28 - 1.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Mathematica

Table[Length[Select[Range[n^2, n^2 - Log[2, n]^2, -1], PrimeQ]], {n, 100}] (* T. D. Noe, Mar 21 2013 *)

Prog

(Python)
import math
def isprime(k):
  s = 3
  while s*s <= k:
    if k%s==0:  return 0
    s+=2
  return 1
for n in range(1, 333):
  c = 0
  top = n*n
  for i in range(top - int(math.log(n, 2)**2), top):
    if i&1:  c += isprime(i)
  print(str(c), end=', ')

Crossrefs

Cf. A094189, A216265, A217317.

Sequence in context: A100890 A262815 A076494 * A071862 A030362 A007906

Adjacent sequences: A217718 A217719 A217720 * A217722 A217723 A217724

Keyword

nonn

Author

Alex Ratushnyak, Mar 21 2013

Status

approved