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
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved