A162145 a(n) = the number of noncomposites (primes or 1) that are n digits long when written in binary.

1, 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

Offset

1,2

Links

Lei Zhou, Table of n, a(n) for n = 1..47

Formula

a(n) = A036378(n-1), n>2. - R. J. Mathar, Jun 27 2009

Example

The consecutive primes 17 (10001 in binary), 19 (10011 in binary), 23 (10111 in binary), 29 (11101 in binary), and 31 (11111 in binary) are the only primes each written with exactly 5 digits in binary. There are 5 of these primes, so a(5) = 5.

Mathematica

Table[PrimePi[2^(d + 1)] - PrimePi[2^d-1], {d, 1, 46}] (*Lei Zhou Dec 17 2013; this is capable of generating terms 1..47 *)
Join[{1, 2}, t=Table[PrimePi[2^n], {n, 2, 40}]; Rest@t - Most@t] (* Vincenzo Librandi, Dec 08 2015 *)

Prog

(Magma) [#PrimesInInterval(2^n, 2^(n+1)): n in [0..25]]; // Vincenzo Librandi, Dec 08 2015

Crossrefs

Cf. A004676.

Same as A036378 except for a(1). - Franklin T. Adams-Watters, May 25 2010

Sequence in context: A240540 A039878 A365616 * A208050 A322176 A039886

Adjacent sequences: A162142 A162143 A162144 * A162146 A162147 A162148

Keyword

base,nonn

Author

Leroy Quet, Jun 25 2009

Extensions

More terms from Franklin T. Adams-Watters, May 25 2010

Status

approved