A177718 a(n) = |(number of 1's in binary representation of prime(n)) - (number of 0's in binary representation of prime(n))|.

0, 2, 1, 3, 2, 2, 1, 1, 3, 3, 5, 0, 0, 2, 4, 2, 4, 4, 1, 1, 1, 3, 1, 1, 1, 1, 3, 3, 3, 1, 7, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 6, 2, 0, 2, 2, 6, 2, 2, 2, 6, 2, 6, 5, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 3, 3, 1, 3, 5, 3, 5, 7, 1, 1, 1, 1, 1, 1, 5, 1, 5, 5, 1, 1, 3, 5, 3, 7, 5, 5, 5, 7, 7, 4, 2, 0, 2, 0, 0, 0, 2

Offset: 1

Author

Juri-Stepan Gerasimov, May 12 2010, May 18 2010

Keywords

• nonn
• base

Examples

			a(1)=0 because 2 = 10_2 and abs(1-1) = 0;
a(2)=2 because 3 = 11_2 and abs(0-2) = 2;
a(3)=1 because 5 = 101_2 and abs(1-2) = 1.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000120, A004676.

Programs

Maple

A023416 := proc(n) a := 0 ; for d in convert(n,base,2) do if d = 0 then a := a+1 ; end if; end do; a ; end proc:
A000120 := proc(n) a := 0 ; for d in convert(n,base,2) do if d = 1 then a := a+1 ; end if; end do; a ; end proc:
A037861 := proc(n) A023416(n)-A000120(n) ; end proc:
A177718 := proc(n) abs(A037861(ithprime(n))) ; end proc: seq(A177718(n),n=1..120) ; # R. J. Mathar, May 15 2010
# second Maple program:
a:= n-> abs(add(2*i-1, i=Bits[Split](ithprime(n)))):
seq(a(n), n=1..105);  # Alois P. Heinz, Jan 18 2022

Mathematica

nzmnu[n_]:=Module[{z=DigitCount[n,2,0]},Abs[2z-IntegerLength[n,2]]]; nzmnu/@ Prime[Range[110]] (* Harvey P. Dale, Feb 15 2015 *)

Python

from sympy import isprime
print([abs(bin(n)[2:].count("1") - bin(n)[2:].count("0")) for n in range (0,1000) if isprime(n)]) # Karl-Heinz Hofmann, Jan 18 2022

Formula

a(n) = abs(A014499(n) - A035103(n)).

a(n) = abs(A037861(prime(n))). - R. J. Mathar, May 15 2010

Extensions

Corrected at three or more places by R. J. Mathar, May 15 2010