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A374403
Number of n-bit primes.
0
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.
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).
Sequence in context: A039878 A365616 A162145 * A208050 A322176 A039886
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Jul 07 2024
STATUS
approved