%I #8 Jan 11 2020 05:45:10
%S 1,1,2,7,13,35,71,147,298,622,1270,2558,5257,10509,21297,42852,86258,
%T 173528,348187,699590,1404936,2818606,5657411,11345622,22746823,
%U 45605127,91421299,183206338,367111951,735525895,1473503602,2951661316,5911864292,11840082252
%N Write the primes in binary; a(n) = total number of 0's in those which have an n-bit expansion.
%e a(2) = 1: 2 = 10 and 3 = 11, with a total of one 0.
%e a(3) = 1: 5 = 101, 7 = 111, again with just one 0.
%t a[n_] := Sum[If[PrimeQ[k], DigitCount[k, 2, 0], 0], {k, 2^(n - 1), 2^n - 1}]; Array[a, 20, 2] (* _Amiram Eldar_, Jan 11 2020 *)
%o (PARI) a(n) = {nb = 0; for (i=2^(n-1), 2^n-1, if (isprime(i), nb += n - norml2(binary(i)));); return (nb);} \\ _Michel Marcus_, Jun 20 2013
%Y Cf. A168156.
%K base,nonn
%O 2,3
%A Jacob Woolcutt (woolcutt(AT)uiuc.edu), Sep 19 2003
%E a(27)-a(35) from _Amiram Eldar_, Jan 11 2020