

A050216


Number of primes between (prime(n))^2 and (prime(n+1))^2, with a(0) = 2 by convention.


9



2, 2, 5, 6, 15, 9, 22, 11, 27, 47, 16, 57, 44, 20, 46, 80, 78, 32, 90, 66, 30, 106, 75, 114, 163, 89, 42, 87, 42, 100, 354, 99, 165, 49, 299, 58, 182, 186, 128, 198, 195, 76, 356, 77, 144, 75, 463, 479, 168, 82, 166, 270, 90, 438, 275, 274, 292, 91, 292, 199, 99
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,1


COMMENTS

The function in Brocard's Conjecture.
The lines in the graph correspond to prime gaps of 2, 4, 6,...  T. D. Noe, Feb 04 2008
Lengths of blocks of consecutive primes in A000430 (union of primes and squares of primes). [Reinhard Zumkeller, Sep 23 2011]
In the nth step of the Eratosthenes' sieve, all multiples of prime(n) are removed. Then a(n) gives the number of new primes obtained after the nth step.  JeanChristophe HervĂ©, Oct 27 2013


LINKS

T. D. Noe, Table of n, a(n) for n=0..10000
Eric Weisstein's World of Mathematics, Brocard's Conjecture


EXAMPLE

There are 2 primes less than 2^2, there are 2 primes between 2^2 and 3^2, 5 primes between 3^2 and 5^2, etc.


MATHEMATICA

PrimePi[ Prime[ n+1 ]^2 ]PrimePi[ Prime[ n ]^2 ]


PROG

(Haskell)
import Data.List (group)
a050216 n = a050216_list !! (n1)
a050216_list =
map length $ filter (/= [0]) $ group $ map a010051 a000430_list
 Reinhard Zumkeller, Sep 23 2011


CROSSREFS

First differences of A000879. Cf. A089609.
Cf. A010051, A001248.
Sequence in context: A147766 A034420 A028410 * A080880 A120843 A205674
Adjacent sequences: A050213 A050214 A050215 * A050217 A050218 A050219


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


EXTENSIONS

Edited by N. J. A. Sloane, Nov 15 2009
Example corrected by Jonathan Sperry, Aug 30 2013


STATUS

approved



