login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of primes that are not less than prime(n)-Log2(n) and not greater than prime(n)+Log2(n), where Log2=A000523.
3

%I #12 Feb 07 2023 08:18:41

%S 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,

%T 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,

%U 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

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

%H Robert Israel, <a href="/A098396/b098396.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%e a(10) = #{p prime: A098386(10) <= p <= A098387(10)} =

%e = #{p prime: 26 <= p <= 32} = #{29,31} = 2.

%p f:= proc(n) local p,d;

%p p:= ithprime(n); d:= ilog2(n);

%p numtheory:-pi(p+d)-numtheory:-pi(p-d-1)

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Aug 13 2018

%t a[n_] := With[{p = Prime[n], d = BitLength[n]-1}, PrimePi[p+d] - PrimePi[p-d-1]];

%t Table[a[n], {n, 1, 200}] (* _Jean-François Alcover_, Feb 07 2023 *)

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Sep 06 2004