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Search: id:A053832
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| A053832 |
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Sum of digits of n written in base 12. |
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+0
3
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| 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 7, 8
(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->{0,1,2,3,4,5,6,7,8,9,10,11}, 1->{1,2,3,4,5,6,7,8,9,10,11,12}, 2->{2,3,4,5,6,7,8,9,10,11,12,13}, etc. - Robert G. Wilson v Jul 27 2006.
a(n) = A138530(n,12) for n > 11. - 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, Duodecimal
Eric Weisstein's World of Mathematics, Digit Sum
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FORMULA
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a(0)=0, a(12n+i)=a(n)+i 0<=i<=11; a(n)=n-11*(sum(k>0, floor(n/12^k))=n-11*A064459 (n). - Benoit Cloitre, Dec 19, 2002
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EXAMPLE
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a(20)=1+8=9 because 20 is written as 18 base 12
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MATHEMATICA
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Table[Plus @@ IntegerDigits[n, 12], {n, 0, 85}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 11}]] &, {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%12, a(n-1)+1, a(n/12)))
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CROSSREFS
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Cf. A000120, A007953.
Sequence in context: A130024 A131232 A010881 this_sequence A056961 A043271 A062759
Adjacent sequences: A053829 A053830 A053831 this_sequence A053833 A053834 A053835
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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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