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Search: id:A053830
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| A053830 |
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Sum of digits of n written in base 9. |
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+0
4
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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; listen)
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OFFSET
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0,3
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COMMENT
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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
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Eric Weisstein's World of Mathematics, Digit Sum
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FORMULA
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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
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EXAMPLE
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a(20)=2+2=4 because 20 is written as 22 base 9
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MATHEMATICA
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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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PROGRAM
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(PARI) a(n)=if(n<1, 0, if(n%9, a(n-1)+1, a(n/9)))
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CROSSREFS
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Cf. A000120, A007953.
Sequence in context: A053844 A010887 A101412 this_sequence A033929 A025482 A023125
Adjacent sequences: A053827 A053828 A053829 this_sequence A053831 A053832 A053833
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KEYWORD
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base,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000
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