OFFSET
1,3
COMMENTS
A famous Japanese mathematics book states that this sequence is nonzero (for n>1) if the Riemann Hypothesis is true, but this statement seems to be false.
If the n-th prime is denoted by p(n) then a(j) = number of nonzero values of floor (j^2/p(n)), over all n >= 1, (derived from A165974). - Christopher Hunt Gribble, Oct 03 2009
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
For n = 5: between 5+1 = 6 and 5^2-1 = 24 there are the following six primes: 7, 11, 13, 17, 19, 23.
MAPLE
P:=proc(n) local i, j, np; for i from 1 by 1 to n do np:=0; for j from i+1 by 1 to i^2-1 do if isprime(j) then np:=np+1; fi; od; print(np); od; end: P(100);
MATHEMATICA
a[n_] := PrimePi[n^2 - 1] - PrimePi[n]; Array[a, 59] (* Robert G. Wilson v, Apr 06 2006 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Mar 22 2006
STATUS
approved