A086904 Write the primes in binary; a(n) = total number of 0's in those which have an n-bit expansion.

1, 1, 2, 7, 13, 35, 71, 147, 298, 622, 1270, 2558, 5257, 10509, 21297, 42852, 86258, 173528, 348187, 699590, 1404936, 2818606, 5657411, 11345622, 22746823, 45605127, 91421299, 183206338, 367111951, 735525895, 1473503602, 2951661316, 5911864292, 11840082252

Offset: 2

Author

Jacob Woolcutt (woolcutt(AT)uiuc.edu), Sep 19 2003

Keywords

• base
• nonn

Examples

			a(2) = 1: 2 = 10 and 3 = 11, with a total of one 0.
a(3) = 1: 5 = 101, 7 = 111, again with just one 0.
		

Crossrefs

Cf. A168156.

Programs

Mathematica

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 *)

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

Extensions

a(27)-a(35) from Amiram Eldar, Jan 11 2020