A053832 Sum of digits of n written in base 12.

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

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

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Jeffrey O. Shallit, Problem 6450, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 59-60; Two series, solution to Problem 6450, ibid., Vol. 92, No. 7 (1985), pp. 513-514.

Robert Walker, Self Similar Sloth Canon Number Sequences.

Eric Weisstein's World of Mathematics, Duodecimal.

Eric Weisstein's World of Mathematics, Digit Sum.

Formula

From Benoit Cloitre, Dec 19 2002: (Start)

a(0) = 0, a(12n+i) = a(n)+i for 0 <= i <= 11.

a(n) = n-11*(Sum_{k>0} floor(n/12^k)) = n-11*A064459(n). (End)

a(n) = A138530(n,12) for n > 11. - Reinhard Zumkeller, Mar 26 2008

Sum_{n>=1} a(n)/(n*(n+1)) = 12*log(12)/11 (Shallit, 1984). - Amiram Eldar, Jun 03 2021

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(n-1)+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, A064459, A138530.

Sequence in context: A297238 A010881 A190600 * A345672 A322094 A056961

Adjacent sequences: A053829 A053830 A053831 * A053833 A053834 A053835

Keyword

base,nonn

Author

Henry Bottomley, Mar 28 2000

Status

approved