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A217721
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Number of primes between n^2 - log_2(n)^2 and n^2 (inclusive).
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1
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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
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OFFSET
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1,7
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COMMENTS
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Conjecture: a(n) > 0 for n > 1.
Conjecture checked up to n = 2^28 - 1.
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LINKS
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MATHEMATICA
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Table[Length[Select[Range[n^2, n^2 - Log[2, n]^2, -1], PrimeQ]], {n, 100}] (* T. D. Noe, Mar 21 2013 *)
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PROG
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(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)+', ',
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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