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

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

1,2

Comments

Partial sums of A168156.

Links

Table of n, a(n) for n=1..34.

Formula

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

Example

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.

Prog

(PARI) s=0; L=p=2; while( L*=2, print1(s", "); until( L<p=nextprime(p+1), s+=norml2(binary(p))))

Crossrefs

Cf. A168153.

Sequence in context: A298612 A340627 A350520 * A005735 A208436 A297015

Adjacent sequences: A168152 A168153 A168154 * A168156 A168157 A168158

Keyword

nonn,base

Author

M. F. Hasler, Nov 20 2009

Extensions

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

Status

approved