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%I #8 Mar 02 2015 02:13:16
%S 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,
%T 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,
%U 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
%N a(n) = 1 if the binary weight of n is prime, otherwise 0.
%F a(n) = A010051(A000120(n)). - _R. J. Mathar_, Apr 09 2008
%e a(0) = 0 (binary). Bits set = 0, 0 not prime -> 0.
%e a(1) = 1 (binary). Bits set = 1, 1 not prime -> 0.
%e a(2) = 10 (binary). Bits set = 1, 1 not prime -> 0.
%e a(3) = 11 (binary). Bits set = 2, 2 prime -> 1.
%p 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
%t Table[If[PrimeQ[Plus @@ IntegerDigits[n, 2]], 1, 0], {n, 0, 100}] (* _Stefan Steinerberger_, Apr 09 2008 *)
%o (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
%Y Begins the same as A135136, but differs starting at a(31).
%K nonn,easy,base
%O 0,1
%A _George Pollard_, Apr 07 2008
%E More terms from _R. J. Mathar_ and _Stefan Steinerberger_, Apr 09 2008