A374403 Number of n-bit primes.

0, 2, 2, 2, 5, 7, 13, 23, 43, 75, 137, 255, 464, 872, 1612, 3030, 5709, 10749, 20390, 38635, 73586, 140336, 268216, 513708, 985818, 1894120, 3645744, 7027290, 13561907, 26207278, 50697537, 98182656, 190335585, 369323305, 717267168, 1394192236, 2712103833, 5279763824

Offset

1,2

Comments

Number of primes whose binary expansion is n digits long.

a(n) is the number of primes in the half-open interval [2^(n-1), 2^n).

First differences of A185192.

See A007053 for additional information.

Links

Table of n, a(n) for n=1..38.

Formula

a(n) = A162145(n) for n >= 2. - Amiram Eldar, Jul 08 2024

Example

a(1) = 0 because neither 0 nor 1 is a prime.
a(2) = 2 because the 2-bit primes are 10_2 = 2 and 11_2 = 3.
a(4) = 2 because the 4-bit primes are 1011_2 = 11 and 1101_2 = 13.

Mathematica

a[n_]:=Sum[Boole[PrimeQ[i]], {i, 2^(n-1), 2^n-1}]; Array[a, 38] (* Stefano Spezia, Jul 07 2024 *

Crossrefs

Essentially the same as A036378 and A162145.

Cf. A185192 (partial sums).

Cf. A000720, A007053.

Sequence in context: A039878 A365616 A162145 * A208050 A322176 A039886

Adjacent sequences: A374400 A374401 A374402 * A374404 A374405 A374406

Keyword

nonn

Author

Jon E. Schoenfield, Jul 07 2024

Status

approved