A095375 Total number of 1's in the binary expansions of the first n primes: summatory A014499.

1, 3, 5, 8, 11, 14, 16, 19, 23, 27, 32, 35, 38, 42, 47, 51, 56, 61, 64, 68, 71, 76, 80, 84, 87, 91, 96, 101, 106, 110, 117, 120, 123, 127, 131, 136, 141, 145, 150, 155, 160, 165, 172, 175, 179, 184, 189, 196, 201, 206, 211, 218, 223, 230, 232, 236, 240, 245, 249, 253

Offset: 1

Author

Labos Elemer, Jun 07 2004

Keywords

• nonn
• base

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A000788, A079584, A014499.

Programs

Maple

read("transforms") :
A095375 := proc(n)
    local a;
    a := 0 ;
    for i from 1 to n do
        a := a+wt(ithprime(i)) ;
    end do:
end proc: # R. J. Mathar, Jul 13 2012
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)
      +add(i, i=Bits[Split](ithprime(n))))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 26 2021

Mathematica

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

PARI

a(n)=my(s);forprime(p=2,prime(n),s+=hammingweight(p));s \\ Charles R Greathouse IV, Mar 29 2013

Python

from sympy import primerange, prime
def A095375(n): return sum(p.bit_count() for p in primerange(prime(n)+1)) # Chai Wah Wu, Nov 12 2024