Search: id:A053828
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%I A053828
%S A053828 0,1,2,3,4,5,6,1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,
%T A053828 10,5,6,7,8,9,10,11,6,7,8,9,10,11,12,1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,
%U A053828 6,7,8,9,4,5,6,7,8,9,10,5,6,7,8,9,10,11,6,7,8,9,10,11,12,7,8,9,10,11
%N A053828 Sum of digits of n written in base 7.
%C A053828 Also the fixed point of the morphism 0->{0,1,2,3,4,5,6}, 1->{1,2,3,4,
               5,6,7}, 2->{2,3,4,5,6,7,8}, etc. - Robert G. Wilson v Jul 27 2006.
%C A053828 a(n) = A138530(n,7) for n > 6. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Mar 26 2008
%H A053828 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitSum.html">Digit Sum</a>
%F A053828 a(0)=0, a(7n+i)=a(n)+i 0<=i<=6; a(n)=n-6*(sum(k>0, floor(n/7^k))=n-6*A054896(n). 
               - Benoit Cloitre, Dec 19, 2002
%e A053828 a(20)=2+6=8 because 20 is written as 26 base 7
%t A053828 Table[Plus @@ IntegerDigits[n, 7], {n, 0, 100}] (* or *)
%t A053828 Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 6}]] &, {0}, 4] 
               (* Robert G. Wilson v Jul 27 2006 *)
%o A053828 (PARI) a(n)=if(n<1,0,if(n%7,a(n-1)+1,a(n/7)))
%Y A053828 Cf. A000120, A007953.
%Y A053828 Sequence in context: A030998 A053842 A010885 this_sequence A033927 A104414 
               A125934
%Y A053828 Adjacent sequences: A053825 A053826 A053827 this_sequence A053829 A053830 
               A053831
%K A053828 base,nonn
%O A053828 0,3
%A A053828 Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000

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