A137331 a(n) = 1 if the binary weight of n is prime, otherwise 0.

0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1

Offset: 0

Author

George Pollard, Apr 07 2008

Keywords

• nonn
• easy
• base

Examples

			a(0) = 0 (binary). Bits set = 0, 0 not prime -> 0.
a(1) = 1 (binary). Bits set = 1, 1 not prime -> 0.
a(2) = 10 (binary). Bits set = 1, 1 not prime -> 0.
a(3) = 11 (binary). Bits set = 2, 2 prime -> 1.
		

Crossrefs

Begins the same as A135136, but differs starting at a(31).

Programs

Maple

A000120 := proc(n) add(i,i=convert(n,base,2)) ; end: A010051 := proc(n) if isprime(n) then 1 ; else 0 ; fi ; end: A137331 := proc(n) A010051(A000120(n)) ; end: seq(A137331(n),n=0..200) ; # R. J. Mathar, Apr 09 2008

Mathematica

Table[If[PrimeQ[Plus @@ IntegerDigits[n, 2]], 1, 0], {n, 0, 100}] (* Stefan Steinerberger, Apr 09 2008 *)

PARI

f(n)={v=binary(n);s=0;for(k=1,#v,if(v[k]== 1,s++));return(isprime(s))};for(n=0,104,if(f(n),print1("1, "),print1("0, "))) \\ Washington Bomfim, Jan 14 2011

Formula

a(n) = A010051(A000120(n)). - R. J. Mathar, Apr 09 2008

Extensions

More terms from R. J. Mathar and Stefan Steinerberger, Apr 09 2008