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A077463 Number of primes p such that n < p < 2n-2. 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 (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
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
Cf. A060715.
Sequence in context: A025792 A119447 A157720 * A084556 A084506 A071578
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Nov 05 2002
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)