

A168156


Sum of the binary digits of all primes between 2^(n1) and 2^n1, i.e., with exactly n binary digits.


2



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
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OFFSET

1,2


COMMENTS

Sequence A168155 yields the partial sums.


LINKS

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


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


PROG

(PARI) s=0; L=p=2; while( L*=2, print1(s", "); s=0; until( L<p=nextprime(p+1), s+=norml2(binary(p))))
(PARI) a(n)=my(s); forprime(p=2^(n1), 2^n1, s+=hammingweight(p)); s \\ Charles R Greathouse IV, Apr 07 2020


CROSSREFS

Cf. A086904.
Sequence in context: A192119 A050563 A282809 * A295403 A272440 A276704
Adjacent sequences: A168153 A168154 A168155 * A168157 A168158 A168159


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Nov 20 2009


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


STATUS

approved



