A095375 - OEIS

%I #19 Nov 13 2024 17:16:17

%S 1,3,5,8,11,14,16,19,23,27,32,35,38,42,47,51,56,61,64,68,71,76,80,84,

%T 87,91,96,101,106,110,117,120,123,127,131,136,141,145,150,155,160,165,

%U 172,175,179,184,189,196,201,206,211,218,223,230,232,236,240,245,249,253

%N Total number of 1's in the binary expansions of the first n primes: summatory A014499.

%H Amiram Eldar, <a href="/A095375/b095375.txt">Table of n, a(n) for n = 1..10000</a>

%e n=4: first 4 primes={10,11,101,111}, with a(4)=8 digits 1.

%p read("transforms") :

%p A095375 := proc(n)

%p     local a;

%p     a := 0 ;

%p     for i from 1 to n do

%p         a := a+wt(ithprime(i)) ;

%p     end do:

%p end proc: # _R. J. Mathar_, Jul 13 2012

%p # second Maple program:

%p a:= proc(n) option remember; `if`(n=0, 0, a(n-1)

%p       +add(i, i=Bits[Split](ithprime(n))))

%p     end:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jun 26 2021

%t lib[x_] :=Count[IntegerDigits[x, 2], 1] {s=0, ta=Table[0, {256}]}; Do[s=s+lib[Prime[n]]; ta[[n]]=s, {n, 1, 256}] ta

%o (PARI) a(n)=my(s);forprime(p=2,prime(n),s+=hammingweight(p));s \\ _Charles R Greathouse IV_, Mar 29 2013

%o (Python)

%o from sympy import primerange, prime

%o def A095375(n): return sum(p.bit_count() for p in primerange(prime(n)+1)) # _Chai Wah Wu_, Nov 12 2024

%Y Cf. A000120, A000788, A079584, A014499.

%K nonn,base

%O 1,2

%A _Labos Elemer_, Jun 07 2004