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

Author

Leroy Quet, Jun 25 2009

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A004676.

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

Programs

Magma

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

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 *)

Formula

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

Extensions

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