This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A168155 #16 Apr 07 2020 10:45:04 %S A168155 0,3,8,14,32,61,117,230,470,922,1807,3597,7071,14022,27693,54876, %T A168155 109077,216301,430183,854696,1700412,3382868,6733230,13404811, %U A168155 26704639,53204936,106034897,211377718,421466683,840573072,1676670824,3345012214,6674425203,13319553281 %N A168155 Sum of binary digits of all primes < 2^n, i.e., with at most n binary digits. %C A168155 Partial sums of A168156. %F A168155 a(n) = A095375( pi( 2^n-1 )), where pi = A000720. %e A168155 No prime can be written with only 1 binary digit, thus a(1)=0. %e A168155 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 A168155 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 A168155 (PARI) s=0; L=p=2; while( L*=2, print1(s", "); until( L<p=nextprime(p+1), s+=norml2(binary(p)))) %Y A168155 Cf. A168153. %K A168155 nonn,base %O A168155 1,2 %A A168155 _M. F. Hasler_, Nov 20 2009 %E A168155 a(25)-a(32) from _Donovan Johnson_, Jul 28 2010 %E A168155 a(33) from _Chai Wah Wu_, Apr 06 2020 %E A168155 a(34) from _Chai Wah Wu_, Apr 07 2020