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Search: id:A053735
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| A053735 |
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Sum of digits of (n written in base 3). |
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+0
20
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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.
a(A062318(n)) = n and a(m) < n for m < A062318(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 26 2008
a(n) = A138530(n,3) for n > 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 26 2008
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..10000
Michael Gilleland, Some Self-Similar Integer Sequences
Eric Weisstein's World of Mathematics, Digit Sum
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FORMULA
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a(0)=0, a(3n)=a(n), a(3n+1)=a(n)+1, a(3n+2)=a(n)+2. - Benoit Cloitre, Dec 19 2002
a(n) = A062756(n) + 2*A081603(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 23 2003
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
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
First differences of A094345. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 08 2005
a(n)=n-2*sum(k>0, floor(n/3^k))=n-2*A054861(n). - Benoit Cloitre, Dec 19, 2002
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EXAMPLE
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a(20)=2+0+2=4 because 20 is written as 202 base 3
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MATHEMATICA
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Table[Plus @@ IntegerDigits[n, 3], {n, 0, 100}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> {a, a+1, a + 2}] &, {0}, 5] (* Robert G. Wilson v Jul 27 2006 *)
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PROGRAM
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(PARI) a(n)=if(n<1, 0, a(n\3)+n%3) - Michael Somos Mar 06 2004
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CROSSREFS
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Cf. A000120, A007953, A053737, A065363. See A134451 for iterations.
Cf. A007089.
Sequence in context: A067731 A147844 A130634 this_sequence A033667 A033923 A116939
Adjacent sequences: A053732 A053733 A053734 this_sequence A053736 A053737 A053738
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KEYWORD
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base,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000
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