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

Author

M. F. Hasler, Nov 20 2009

Keywords

• nonn
• base

Comments

Partial sums of A168156.

Examples

			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.
		

Crossrefs

Cf. A168153.

Programs

PARI

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

Formula

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

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