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A075699
Number of primes in the interval (n,4n].
2
2, 3, 3, 4, 5, 6, 5, 7, 7, 8, 9, 10, 9, 10, 11, 12, 12, 13, 13, 14, 15, 15, 15, 15, 16, 18, 19, 20, 20, 20, 19, 20, 21, 21, 23, 23, 22, 24, 24, 25, 25, 26, 25, 26, 27, 28, 27, 28, 29, 31, 31, 31, 31, 31, 31, 32, 33, 34, 34, 35, 35, 35, 36, 36, 37, 38, 37, 39, 39, 40, 41, 41, 40
OFFSET
1,1
COMMENTS
Difference a(n+1) - a(n) = -1, 0, 1, 2, ... .
LINKS
Madhuparna Das and Goutam Paul, Revisiting Generalized Bertand's Postulate and Prime Gaps, arXiv:1710.09891 [math.NT], 2017-2019.
FORMULA
a(n) = A000720(4n) - A000720(n). - Michel Marcus, Oct 02 2013
EXAMPLE
a(4) = 4 because between 4 and 16 there are 4 primes: 5, 7, 11, 13.
a(7) = 5 because between 7 and 28 there are 5 primes: 11, 13, 17, 19, 23.
MAPLE
A075699 := proc(n)
numtheory[pi](4*n)-numtheory[pi](n) ;
end proc: # R. J. Mathar, Nov 03 2017
MATHEMATICA
s=4; a[n_] := PrimePi[s*n]-PrimePi[n]
PROG
(PARI) a(n) = primepi(4*n) - primepi(n); \\ Michel Marcus, Oct 02 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 02 2002
STATUS
approved