cp's OEIS Frontend

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

%I A162145 #19 Sep 08 2022 08:45:46
%S A162145 1,2,2,2,5,7,13,23,43,75,137,255,464,872,1612,3030,5709,10749,20390,
%T A162145 38635,73586,140336,268216,513708,985818,1894120,3645744,7027290,
%U A162145 13561907,26207278,50697537,98182656,190335585,369323305,717267168
%N A162145 a(n) = the number of noncomposites (primes or 1) that are n digits long when written in binary.
%H A162145 Lei Zhou, <a href="/A162145/b162145.txt">Table of n, a(n) for n = 1..47</a>
%F A162145 a(n) = A036378(n-1), n>2. - _R. J. Mathar_, Jun 27 2009
%e A162145 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.
%t A162145 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 *)
%t A162145 Join[{1, 2}, t=Table[PrimePi[2^n], {n, 2, 40}]; Rest@t - Most@t] (* _Vincenzo Librandi_, Dec 08 2015 *)
%o A162145 (Magma) [#PrimesInInterval(2^n, 2^(n+1)): n in [0..25]]; // _Vincenzo Librandi_, Dec 08 2015
%Y A162145 Cf. A004676.
%Y A162145 Same as A036378 except for a(1). - _Franklin T. Adams-Watters_, May 25 2010
%K A162145 base,nonn
%O A162145 1,2
%A A162145 _Leroy Quet_, Jun 25 2009
%E A162145 More terms from _Franklin T. Adams-Watters_, May 25 2010