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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 (list; graph; refs; listen; history; text; internal format)
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)=n-8*(sum(k>0, floor(n/9^k))=n-8*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(n-1)+1, a(n/9)))

CROSSREFS

Cf. A000120, A007953, A053735, A053737, A053824, A053828, A231684-A231687.

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

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Last modified February 20 01:06 EST 2018. Contains 299357 sequences. (Running on oeis4.)