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

0,1

Links

Table of n, a(n) for n=0..104.

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A350866 A252743 A135136 * A093386 A219098 A288710

Adjacent sequences: A137328 A137329 A137330 * A137332 A137333 A137334

Keyword

nonn,easy,base

Author

George Pollard, Apr 07 2008

Extensions

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

Status

approved