

A053830


Sum of digits of (n written in base 9).


17



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, 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, 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
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OFFSET

0,3


COMMENTS

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
a(n) = A138530(n,9) for n > 8.  Reinhard Zumkeller, Mar 26 2008


LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..59049
Robert Walker, Self Similar Sloth Canon Number Sequences
Eric Weisstein's World of Mathematics, Digit Sum


FORMULA

a(0)=0, a(9n+i)=a(n)+i 0<=i<=8; a(n)=n8*(sum(k>0, floor(n/9^k))=n8*A054898(n).  Benoit Cloitre, Dec 19 2002
a(n)=Sum_k>=0 {A031087(n,k)}.  Philippe Deléham, Oct 21 2011


EXAMPLE

a(20)=2+2=4 because 20 is written as 22 base 9
From Omar E. Pol, Feb 23 2010: (Start)
It appears that this can be written as a triangle (See the conjecture in the entry A000120):
0;
1,2,3,4,5,6,7,8;
1,2,3,4,5,6,7,8,9,2,3,4,5,6,7,8,9,10,3,4,5,6,7,8,9,10,11,4,5,6,7,8,9,10,11...
where the rows converge to A173529. (End)


MATHEMATICA

Table[Plus @@ IntegerDigits[n, 9], {n, 0, 100}] (* or *)
Nest[ Flatten[ #1 /. a_Integer > Table[a + i, {i, 0, 8}]] &, {0}, 3] (* Robert G. Wilson v, Jul 27 2006 *)


PROG

(PARI) a(n)=if(n<1, 0, if(n%9, a(n1)+1, a(n/9)))


CROSSREFS

Cf. A000120, A007953, A053735, A053737, A053824, A053828, A231684A231687.
Cf. A173529.  Omar E. Pol, Feb 23 2010
Sequence in context: A053844 A010887 A101412 * A033929 A025482 A023125
Adjacent sequences: A053827 A053828 A053829 * A053831 A053832 A053833


KEYWORD

base,nonn


AUTHOR

Henry Bottomley, Mar 28 2000


STATUS

approved



