Search: id:A053830
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%I A053830
%S A053830 0,1,2,3,4,5,6,7,8,1,2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,10,3,4,5,6,7,8,9,
%T A053830 10,11,4,5,6,7,8,9,10,11,12,5,6,7,8,9,10,11,12,13,6,7,8,9,10,11,12,13,
%U A053830 14,7,8,9,10,11,12,13,14,15,8,9,10,11,12,13,14,15,16,1,2,3,4,5,6,7,8,9
%N A053830 Sum of digits of n written in base 9.
%C A053830 Also the fixed point of the morphism 0->{0,1,2,3,4,5,6,7,8}, 1->{1,2,
               3,4,5,6,7,8,9}, 2->{2,3,4,5,6,7,8,9,10}, etc. - Robert G. Wilson 
               v Jul 27 2006.
%C A053830 a(n) = A138530(n,9) for n > 8. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 26 2008
%H A053830 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitSum.html">Digit Sum</a>
%F A053830 a(0)=0, a(9n+i)=a(n)+i 0<=i<=8; a(n)=n-8*(sum(k>0, floor(n/9^k))=n-8*A054898(n). 
               - Benoit Cloitre, Dec 19, 2002
%e A053830 a(20)=2+2=4 because 20 is written as 22 base 9
%t A053830 Table[Plus @@ IntegerDigits[n, 9], {n, 0, 100}] (* or *)
%t A053830 Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 8}]] &, {0}, 3] 
               (* Robert G. Wilson v Jul 27 2006 *)
%o A053830 (PARI) a(n)=if(n<1,0,if(n%9,a(n-1)+1,a(n/9)))
%Y A053830 Cf. A000120, A007953.
%Y A053830 Sequence in context: A053844 A010887 A101412 this_sequence A033929 A025482 
               A023125
%Y A053830 Adjacent sequences: A053827 A053828 A053829 this_sequence A053831 A053832 
               A053833
%K A053830 base,nonn
%O A053830 0,3
%A A053830 Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000

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