cp's OEIS Frontend

A143070 A positive integer n is included if the number of 0's in the binary representation of n is a power of 2 (including being possibly 1).

%I A143070 #18 Oct 26 2017 14:39:35
%S A143070 2,4,5,6,9,10,11,12,13,14,16,19,21,22,23,25,26,27,28,29,30,33,34,36,
%T A143070 39,40,43,45,46,47,48,51,53,54,55,57,58,59,60,61,62,67,69,70,73,74,76,
%U A143070 79,81,82,84,87,88,91,93,94,95,97,98,100,103,104,107,109,110,111,112,115
%N A143070 A positive integer n is included if the number of 0's in the binary representation of n is a power of 2 (including being possibly 1).
%H A143070 Reinhard Zumkeller, <a href="/A143070/b143070.txt">Table of n, a(n) for n = 1..10000</a>
%F A143070 A209229(A023416(a(n))) = 1. - _Reinhard Zumkeller_, Sep 14 2014
%e A143070 34 in binary is 100010. This has 4 zeros. And since 4 is a power of 2, 34 is included in the sequence.
%p A143070 a:=proc(n) local nn,n0: nn:=convert(n,base,2): n0:=nops(nn)-add(nn[j], j=1.. nops(nn)): if 0 < n0 and type(log[2](n0),integer)=true then n else end if end proc: seq(a(n),n=1..100); # _Emeric Deutsch_, Aug 11 2008
%t A143070 Select[Range@ 120, IntegerQ@ Log2@ DigitCount[#, 2, 0] &] (* _Michael De Vlieger_, Oct 25 2017 *)
%o A143070 (Haskell)
%o A143070 a143070 n = a143070_list !! (n-1)
%o A143070 a143070_list = filter ((== 1) . a209229 . a023416) [1..]
%o A143070 -- _Reinhard Zumkeller_, Sep 14 2014
%o A143070 (PARI) ispow2(n) = (n==1) || (n==2) || (ispower(n,,&k) && (k==2));
%o A143070 isok(n) = ispow2(#binary(n) - hammingweight(n)); \\ _Michel Marcus_, Oct 26 2017
%Y A143070 Cf. A023416, A143071, A143072.
%Y A143070 Cf. A209229.
%K A143070 base,nonn
%O A143070 1,1
%A A143070 _Leroy Quet_, Jul 22 2008
%E A143070 More terms from _Emeric Deutsch_, Aug 11 2008
%E A143070 a(61)-a(68) from _Ray Chandler_, Jun 20 2009