A168156 -id:A168156 - cp's OEIS frontend

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

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

			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.

Cf. A168156.

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 *)

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

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

A168155 Sum of binary digits of all primes < 2^n, i.e., with at most n binary digits.

Original entry on oeis.org

0, 3, 8, 14, 32, 61, 117, 230, 470, 922, 1807, 3597, 7071, 14022, 27693, 54876, 109077, 216301, 430183, 854696, 1700412, 3382868, 6733230, 13404811, 26704639, 53204936, 106034897, 211377718, 421466683, 840573072, 1676670824, 3345012214, 6674425203, 13319553281

Offset: 1

M. F. Hasler, Nov 20 2009

Partial sums of A168156.

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

Cf. A168153.

s=0; L=p=2; while( L*=2, print1(s", "); until( L

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

a(25)-a(32) from Donovan Johnson, Jul 28 2010
a(33) from Chai Wah Wu, Apr 06 2020
a(34) from Chai Wah Wu, Apr 07 2020

cp's OEIS Frontend

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

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