A077463 - OEIS

A077463

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

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

(list; graph; refs; listen; history; text; internal format)

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}] (* Jean-François Alcover, Oct 31 2012 *)

CROSSREFS

Related sequences:

Primes (p) and composites (c): A000040, A002808, A000720, A065855.

Primes between p(n) and 2*p(n): A063124, A070046; between c(n) and 2*c(n): A376761; between n and 2*n: A035250, A060715, A077463, A108954.

Composites between p(n) and 2*p(n): A246514; between c(n) and 2*c(n): A376760; between n and 2*n: A075084, A307912, A307989, A376759.

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