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A053832 Sum of digits of n written in base 12. 10
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; refs; listen; history; text; internal format)
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
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.
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
Sequence in context: A297238 A010881 A190600 * A345672 A322094 A056961
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved

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Last modified March 19 02:55 EDT 2024. Contains 370952 sequences. (Running on oeis4.)