A098396 Number of primes that are not less than prime(n)-Log2(n) and not greater than prime(n)+Log2(n), where Log2=A000523.

1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 3, 2, 2, 2, 1, 2, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 3, 3, 2, 1, 2, 3, 3, 2, 2, 2, 1, 1, 1, 2, 2, 2, 3, 2, 1, 2, 4, 4, 3, 2, 2, 3, 3, 4, 2, 2, 3, 3, 3, 2, 2, 2, 1, 2, 2, 2, 3, 3, 3, 2, 3, 4, 4, 3, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3

Offset: 1

Author

Reinhard Zumkeller, Sep 06 2004

Keywords

• nonn

Examples

			a(10) = #{p prime: A098386(10) <= p <= A098387(10)} =
= #{p prime: 26 <= p <= 32} = #{29,31} = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

f:= proc(n) local p,d;
  p:= ithprime(n); d:= ilog2(n);
  numtheory:-pi(p+d)-numtheory:-pi(p-d-1)
end proc:
map(f, [$1..200]); # Robert Israel, Aug 13 2018

Mathematica

a[n_] := With[{p = Prime[n], d = BitLength[n]-1}, PrimePi[p+d] - PrimePi[p-d-1]];
Table[a[n], {n, 1, 200}] (* Jean-François Alcover, Feb 07 2023 *)

Formula

a(n) = A000720(A098386(n)) - A000720(A098387(n)-1).

A098398(n) <= a(n) <= A098397(n) <= A097935(n).