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

2,3

Links

Table of n, a(n) for n=2..35.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A168156.

Sequence in context: A309368 A051748 A330452 * A358906 A360869 A291276

Adjacent sequences: A086901 A086902 A086903 * A086905 A086906 A086907

Keyword

base,nonn

Author

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

Extensions

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

Status

approved