

A168155


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


1



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
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OFFSET

1,2


COMMENTS

Partial sums of A168156.


LINKS

Table of n, a(n) for n=1..32.


FORMULA

a(n) = A095375( pi( 2^n1 )), 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: A169929 A129067 A298612 * 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


STATUS

approved



