

A077463


Number of primes p such that n < p < 2n2.


3



0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 5, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 9, 9, 10, 10, 11, 11, 11, 12, 13, 13, 14, 13, 13, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 13, 13, 13, 14, 15, 15, 14, 15, 15, 15, 15, 15
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OFFSET

1,8


COMMENTS

a(n) > 0 for n > 3 by Bertrand's postulate (and Chebyshev's proof of 1852).  Jonathan Vos Post, Aug 08 2013


LINKS

Table of n, a(n) for n=1..84.
J. Sondow and E. Weisstein, Bertrand's Postulate, World of Mathematics
M. Tchebichef, Memoire sur les nombres premiers, J. Math. Pures Appliq. 17 (1852) 366.


EXAMPLE

a(19) = 3, the first value smaller than a previous value, because the only primes between 19 and 2 * 19  2 = 36 are {23,29,31}.  Jonathan Vos Post, Aug 08 2013


MATHEMATICA

a[n_] := PrimePi[2n  2]  PrimePi[n]; a[1] = 0; Table[a[n], {n, 1, 100}] (* JeanFrançois Alcover, Oct 31 2012 *)


CROSSREFS

Cf. A060715.
Sequence in context: A025792 A119447 A157720 * A084556 A084506 A071578
Adjacent sequences: A077460 A077461 A077462 * A077464 A077465 A077466


KEYWORD

nonn


AUTHOR

Eric W. Weisstein, Nov 05 2002


STATUS

approved



