%I A053737
%S A053737 0,1,2,3,1,2,3,4,2,3,4,5,3,4,5,6,1,2,3,4,2,3,4,5,3,4,5,6,4,5,6,7,2,3,4,
%T A053737 5,3,4,5,6,4,5,6,7,5,6,7,8,3,4,5,6,4,5,6,7,5,6,7,8,6,7,8,9,1,2,3,4,2,3,
%U A053737 4,5,3,4,5,6,4,5,6,7,2,3,4,5,3,4,5,6,4,5,6,7,5,6,7,8,3,4,5,6,4,5,6,7,5
%N A053737 Sum of digits of (n written in base 4).
%C A053737 Also the fixed point of the morphism 0->{0,1,2,3}, 1->{1,2,3,4}, 2->{2,
               3,4,5}, etc. - Robert G. Wilson v Jul 27 2006.
%C A053737 a(n) = A138530(n,4) for n > 3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 26 2008
%H A053737 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitSum.html">Digit Sum</a>
%F A053737 a(0)=0, a(4n+i)=a(n)+i 0<=i<=3; a(n)=n-3*(sum(k>0, floor(n/4^k))=n-3*A054893(n). 
               - Benoit Cloitre, Dec 19, 2002
%F A053737 G.f.: (Sum_{k>=0} (x^(4^k)+2*x^(2*4^k)+3*x^(3*4^k))/(1+x^(4^k)+x^(2*4^k)+x^(3*4^k))/
               (1-x). - Franklin T. Adams-Watters, Nov 03 2005
%e A053737 a(20)=1+1+0=2 because 20 is written as 110 base 4.
%t A053737 Table[Plus @@ IntegerDigits[n, 4], {n, 0, 100}] (* or *)
%t A053737 Nest[ Flatten[ #1 /. a_Integer -> {a, a+1, a+2, a+3}] &, {0}, 4] (* Robert 
               G. Wilson v Jul 27 2006 *)
%o A053737 (PARI) a(n)=if(n<1,0,if(n%4,a(n-1)+1,a(n/4)))
%Y A053737 Cf. A000120, A007953, A053735.
%Y A053737 Sequence in context: A007720 A129968 A027615 this_sequence A033924 A003315 
               A071797
%Y A053737 Adjacent sequences: A053734 A053735 A053736 this_sequence A053738 A053739 
               A053740
%K A053737 base,nonn
%O A053737 0,3
%A A053737 Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000