Search: id:A053831
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%I A053831
%S A053831 0,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10,11,2,3,4,5,6,7,8,9,10,11,
%T A053831 12,3,4,5,6,7,8,9,10,11,12,13,4,5,6,7,8,9,10,11,12,13,14,5,6,7,8,9,10,
%U A053831 11,12,13,14,15,6,7,8,9,10,11,12,13,14,15,16,7,8,9,10,11,12,13,14,15
%N A053831 Sum of digits of n written in base 11.
%C A053831 Also the fixed point of the morphism 0->{0,1,2,3,4,5,6,7,8,9,10}, 1->
               {1,2,3,4,5,6,7,8,9,10,11}, 2->{2,3,4,5,6,7,8,9,10,11,12}, etc. - 
               Robert G. Wilson v Jul 27 2006.
%C A053831 a(n) = A138530(n,11) for n > 10. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 26 2008
%H A053831 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitSum.html">Digit Sum</a>
%F A053831 a(0)=0, then a(11n+i)=a(n)+i 0<=i<=10; a(n)=n-(m-1)*(sum(k>0, floor(n/
               m^k))=n-(m-1)*A064458 (n). - Benoit Cloitre, Dec 19, 2002
%e A053831 a(20)=1+9=10 because 20 is written as 19 base 11
%t A053831 Table[Plus @@ IntegerDigits[n, 11], {n, 0, 86}] (* or *)
%t A053831 Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 10}]] &, {0}, 2] 
               (* Robert G. Wilson v Jul 27 2006 *)
%o A053831 (PARI) a(n)=if(n<1,0,if(n%11,a(n-1)+1,a(n/11)))
%Y A053831 Cf. A000120, A007953.
%Y A053831 Sequence in context: A010880 A097462 A010889 this_sequence A067453 A118541 
               A084905
%Y A053831 Adjacent sequences: A053828 A053829 A053830 this_sequence A053832 A053833 
               A053834
%K A053831 base,nonn
%O A053831 0,3
%A A053831 Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000

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