Search: id:A053735
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%I A053735
%S A053735 0,1,2,1,2,3,2,3,4,1,2,3,2,3,4,3,4,5,2,3,4,3,4,5,4,5,6,1,2,3,2,3,4,3,4,
%T A053735 5,2,3,4,3,4,5,4,5,6,3,4,5,4,5,6,5,6,7,2,3,4,3,4,5,4,5,6,3,4,5,4,5,6,5,
%U A053735 6,7,4,5,6,5,6,7,6,7,8,1,2,3,2,3,4,3,4,5,2,3,4,3,4,5,4,5,6,3,4,5,4,5,6
%N A053735 Sum of digits of (n written in base 3).
%C A053735 Also the fixed point of the morphism 0->{0,1,2}, 1->{1,2,3}, 2->{2,3,
               4}, etc. - Robert G. Wilson v Jul 27 2006.
%C A053735 a(A062318(n)) = n and a(m) < n for m < A062318(n). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Feb 26 2008
%C A053735 a(n) = A138530(n,3) for n > 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 26 2008
%H A053735 T. D. Noe, <a href="b053735.txt">Table of n, a(n) for n = 0..10000</a>
%H A053735 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%H A053735 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitSum.html">Digit Sum</a>
%F A053735 a(0)=0, a(3n)=a(n), a(3n+1)=a(n)+1, a(3n+2)=a(n)+2. - Benoit Cloitre, 
               Dec 19 2002
%F A053735 a(n) = A062756(n) + 2*A081603(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 23 2003
%F A053735 G.f.: (Sum_{k>=0} (x^(3^k)+2*x^(2*3^k))/(1+x^(3^k)+x^(2*3^k)))/(1-x). 
               - Michael Somos Mar 06 2004, corrected by Franklin T. Adams-Watters, 
               Nov 03 2005
%F A053735 In general, the sum of digits of (n written in base b) has generating 
               function (Sum_{k>=0} (Sum_{0<=i<b} i*x^(i*b^k))/(Sum_{0<=i<b} x^(i*b^k)))/
               (1-x). - Franklin T. Adams-Watters, Nov 03 2005
%F A053735 First differences of A094345. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Nov 08 2005
%F A053735 a(n)=n-2*sum(k>0, floor(n/3^k))=n-2*A054861(n). - Benoit Cloitre, Dec 
               19, 2002
%e A053735 a(20)=2+0+2=4 because 20 is written as 202 base 3
%t A053735 Table[Plus @@ IntegerDigits[n, 3], {n, 0, 100}] (* or *)
%t A053735 Nest[ Flatten[ #1 /. a_Integer -> {a, a+1, a + 2}] &, {0}, 5] (* Robert 
               G. Wilson v Jul 27 2006 *)
%o A053735 (PARI) a(n)=if(n<1,0,a(n\3)+n%3) - Michael Somos Mar 06 2004
%Y A053735 Cf. A000120, A007953, A053737, A065363. See A134451 for iterations.
%Y A053735 Cf. A007089.
%Y A053735 Sequence in context: A067731 A147844 A130634 this_sequence A033667 A033923 
               A116939
%Y A053735 Adjacent sequences: A053732 A053733 A053734 this_sequence A053736 A053737 
               A053738
%K A053735 base,nonn
%O A053735 0,3
%A A053735 Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000

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