A168156 Sum of the binary digits of all primes between 2^(n-1) and 2^n-1, i.e., with exactly n binary digits.

0, 3, 5, 6, 18, 29, 56, 113, 240, 452, 885, 1790, 3474, 6951, 13671, 27183, 54201, 107224, 213882, 424513, 845716, 1682456, 3350362, 6671581, 13299828, 26500297, 52829961, 105342821, 210088965, 419106389, 836097752, 1668341390, 3329412989, 6645128078

Offset: 1

Author

M. F. Hasler, Nov 20 2009

Keywords

• nonn
• base

Comments

Sequence A168155 yields the partial sums.

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 have a total of a(3)=5 nonzero bits.
		

Crossrefs

Cf. A086904.

Programs

PARI

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

PARI

a(n)=my(s); forprime(p=2^(n-1),2^n-1, s+=hammingweight(p)); s \\ Charles R Greathouse IV, Apr 07 2020

Extensions

a(26)-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