%I #16 Apr 07 2020 10:45:04

%S 0,3,8,14,32,61,117,230,470,922,1807,3597,7071,14022,27693,54876,

%T 109077,216301,430183,854696,1700412,3382868,6733230,13404811,

%U 26704639,53204936,106034897,211377718,421466683,840573072,1676670824,3345012214,6674425203,13319553281

%N Sum of binary digits of all primes < 2^n, i.e., with at most n binary digits.

%C Partial sums of A168156.

%F a(n) = A095375( pi( 2^n-1 )), where pi = A000720.

%e No prime can be written with only 1 binary digit, thus a(1)=0.

%e The primes that can be written with 2 binary digits are 2 = 10[2] and 3 = 11[2], they have 3 nonzero bits, so a(2)=3.

%e Primes with 3 binary digits are 5 = 101[2] and 7 = 111[3]. They add 5 more nonzero bits to yield a(3) = a(2)+5 = 8.

%o (PARI) s=0; L=p=2; while( L*=2, print1(s", "); until( L<p=nextprime(p+1), s+=norml2(binary(p))))

%Y Cf. A168153.

%K nonn,base

%O 1,2

%A _M. F. Hasler_, Nov 20 2009

%E a(25)-a(32) from _Donovan Johnson_, Jul 28 2010

%E a(33) from _Chai Wah Wu_, Apr 06 2020

%E a(34) from _Chai Wah Wu_, Apr 07 2020