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A053830
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Sum of digits of n written in base 9.
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5
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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; internal format)
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OFFSET
| 0,3
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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 (reinhard.zumkeller(AT)gmail.com), Mar 26 2008
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LINKS
| Eric Weisstein's World of Mathematics, Digit Sum
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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)}. - From DELEHAM Philippe, Oct 21 2011.
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EXAMPLE
| a(20)=2+2=4 because 20 is written as 22 base 9
Contribution from Omar E. Pol (info(AT)polprimos.com), 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)
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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 *)
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PROG
| (PARI) a(n)=if(n<1, 0, if(n%9, a(n-1)+1, a(n/9)))
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CROSSREFS
| Cf. A000120, A007953.
Cf. A173529. [From Omar E. Pol (info(AT)polprimos.com), Feb 23 2010]
Sequence in context: A053844 A010887 A101412 * A033929 A025482 A023125
Adjacent sequences: A053827 A053828 A053829 * A053831 A053832 A053833
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KEYWORD
| base,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000
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