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Search: id:A053831
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| A053831 |
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Sum of digits of n written in base 11. |
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+0
3
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 9, 10, 11, 12, 13, 14, 15
(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->{0,1,2,3,4,5,6,7,8,9,10}, 1->{1,2,3,4,5,6,7,8,9,10,11}, 2->{2,3,4,5,6,7,8,9,10,11,12}, etc. - Robert G. Wilson v Jul 27 2006.
a(n) = A138530(n,11) for n > 10. - 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, then a(11n+i)=a(n)+i 0<=i<=10; a(n)=n-(m-1)*(sum(k>0, floor(n/m^k))=n-(m-1)*A064458 (n). - Benoit Cloitre, Dec 19, 2002
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EXAMPLE
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a(20)=1+9=10 because 20 is written as 19 base 11
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MATHEMATICA
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Table[Plus @@ IntegerDigits[n, 11], {n, 0, 86}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 10}]] &, {0}, 2] (* 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%11, a(n-1)+1, a(n/11)))
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CROSSREFS
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Cf. A000120, A007953.
Sequence in context: A010880 A097462 A010889 this_sequence A067453 A118541 A084905
Adjacent sequences: A053828 A053829 A053830 this_sequence A053832 A053833 A053834
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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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