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A033052 a(1) = 1, a(2n) = 16a(n), a(2n+1) = a(2n)+1. 19

%I

%S 0,1,16,17,256,257,272,273,4096,4097,4112,4113,4352,4353,4368,4369,

%T 65536,65537,65552,65553,65792,65793,65808,65809,69632,69633,69648,

%U 69649,69888,69889,69904,69905,1048576,1048577,1048592,1048593,1048832

%N a(1) = 1, a(2n) = 16a(n), a(2n+1) = a(2n)+1.

%C Numbers whose set of base 16 digits is {0,1}.

%C a(n) = Xpower(n,4). - _Antti Karttunen_, Apr 26 1999

%C Sums of distinct powers of 16.

%C For every nonnegative n, A000695(n) is a unique sum of the form a(k)+4a(l). Thus every nonnegative n is a unique sum of the form a(p)+2a(q)+4a(r)+8a(s). This gives a one-to-one map of the set N_0 of all nonnegative integers to (N_0)^4. Furthermore, if, for a fixed positive integer m, to consider all sums of distinct powers of 4^m, then one can obtain a one-to-one map of the set N_0 to (N_0)^(2^m). [_Vladimir Shevelev_, Nov 14 2008]

%H Vincenzo Librandi, <a href="/A033052/b033052.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum{d(i)*16^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} is the base 2 representation of n.

%F a(n) = A097262(n)/15.

%F a(2n) = 16*a(n), a(2n+1) = a(2n)+1.

%F a(n) = Sum_k>=0 {A030308(n,k)*16^k}. - _Philippe Deléham_, Oct 19 2011.

%F G.f.: (1/(1 - x))*Sum_{k>=0} 16^k*x^(2^k)/(1 + x^(2^k)). - _Ilya Gutkovskiy_, Jun 04 2017

%t FromDigits[#,16]&/@Tuples[{0,1},5] (* _Vincenzo Librandi_, Jun 04 2012 *)

%o (MAGMA) [n: n in [1..1050000] | Set(IntegerToSequence(n, 16)) subset {0, 1}]; // _Vincenzo Librandi_, May 04 2012

%o (PARI) a(n)=n=Vecrev(binary(n));sum(i=1,#n,n[i]<<(4*i))>>4 \\ _Charles R Greathouse IV_, Sep 23 2012

%Y Cf. A000695, A005836, A033042-A033051.

%Y Column 4 of A048723. Row 15 of array A104257.

%K nonn,base,easy

%O 0,3

%A _Clark Kimberling_

%E Extended by _Ray Chandler_, Aug 03 2004

%E Simpler definition from _Ralf Stephan_, Jun 18 2005

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Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)