%I #22 Jun 11 2024 04:41:20

%S 0,1,2,3,4,9,15,28,50,93,168,305,559,1023,1894,3506,6536,12245,22993,

%T 43383,82017,155603,295939,564155,1077862,2063680,3957800,7603544,

%U 14630834,28192741,54400018,105097555,203280210,393615795,762939100,1480206268,2874398504,5586502337

%N Number of primes between n and 2^n inclusive.

%H Amiram Eldar, <a href="/A284437/b284437.txt">Table of n, a(n) for n = 0..92</a> (terms 0..47 from Vincenzo Librandi)

%F a(n) = A284275(n) + A080339(n) for n >= 1. - _Amiram Eldar_, Jun 11 2024

%e a(0) = 0 because there are 0 primes between 0 and 2^0.

%e a(5) = 9 because there are 9 primes between 5 and 2^5: 5, 7, 11, 13, 17, 19, 23, 29, 31 (we count the boundary of the interval in this case).

%t Join[{0}, f[n_]:=PrimePi[2^n] - PrimePi[n-1]; Array[f, 37]]

%o (Magma) [0] cat [#PrimesInInterval(n, 2^n): n in [1..28]];

%Y Cf. A000720, A007053, A035250, A060715, A080339, A284275.

%K nonn

%O 0,3

%A _Vincenzo Librandi_, Mar 27 2017