

A053832


Sum of digits of n written in base 12.


5



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
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OFFSET

0,3


COMMENTS

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, Mar 26 2008


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Robert Walker, Self Similar Sloth Canon Number Sequences
Eric Weisstein's World of Mathematics, Duodecimal
Eric Weisstein's World of Mathematics, Digit Sum


FORMULA

a(0)=0, a(12n+i)=a(n)+i 0<=i<=11; a(n)=n11*(sum(k>0, floor(n/12^k))=n11*A064459(n).  Benoit Cloitre, Dec 19 2002


EXAMPLE

a(20) = 1 + 8 = 9 because 20 is written as 18 base 12.


MATHEMATICA

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 *)


PROG

(PARI) a(n)=if(n<1, 0, if(n%12, a(n1)+1, a(n/12)))
(Haskell)
a053832 n = q 0 $ divMod n 12 where
q r (0, d) = r + d
q r (m, d) = q (r + d) $ divMod m 12
 Reinhard Zumkeller, May 15 2011


CROSSREFS

Cf. A000120, A007953.
Sequence in context: A297238 A010881 A190600 * A322094 A056961 A297239
Adjacent sequences: A053829 A053830 A053831 * A053833 A053834 A053835


KEYWORD

base,nonn


AUTHOR

Henry Bottomley, Mar 28 2000


STATUS

approved



