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

1,2

Links

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

Example

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

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

Prog

(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

Crossrefs

Cf. A000120, A000788, A079584, A014499.

Sequence in context: A185723 A022852 A180124 * A345979 A129260 A076829

Adjacent sequences: A095372 A095373 A095374 * A095376 A095377 A095378

Keyword

nonn,base

Author

Labos Elemer, Jun 07 2004

Status

approved