OFFSET
0,3
COMMENTS
Also the fixed point of the morphism 0->{0,1,2,3,4,5,6,7}, 1->{1,2,3,4,5,6,7,8}, 2->{2,3,4,5,6,7,8,9}, 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, Digit Sum.
Eric Weisstein's World of Mathematics, Octal.
FORMULA
From Benoit Cloitre, Dec 19 2002: (Start)
a(0) = 0, a(8n+i) = a(n)+i for 0 <= i <= 7.
a(n) = n-7*(Sum_{k>0} floor(n/8^k)) = n-7*A054897(n). (End)
a(n) = A138530(n,8) for n > 7. - Reinhard Zumkeller, Mar 26 2008
a(n) = Sum_k>=0 {A031045(n,k)}. - Philippe Deléham, Oct 21 2011
a(0) = 0; a(n) = a(n - 8^floor(log_8(n))) + 1. - Ilya Gutkovskiy, Aug 24 2019
Sum_{n>=1} a(n)/(n*(n+1)) = 8*log(8)/7 (Shallit, 1984). - Amiram Eldar, Jun 03 2021
EXAMPLE
a(20)=2+4=6 because 20 is written as 24 base 8.
From Omar E. Pol, Feb 21 2010: (Start)
It appears that this can be written as a triangle (See the conjecture in the entry A000120):
0,
1,2,3,4,5,6,7,
1,2,3,4,5,6,7,8,2,3,4,5,6,7,8,9,3,4,5,6,7,8,9,10,4,5,6,7,8,9,10,11,5,6,7,8,9,10,11,12,6,7,8,9,10,11,12,13,7,8,9,10,11,12,13,14,
1,2,3,4,5,6,7,8,2,3,4,5,6,7,8,9,3,4,5,6,7,8,9,10,4,5,6,7,8,9,10...
where the rows converge to A173528. (End)
MATHEMATICA
Table[Plus @@ IntegerDigits[n, 8], {n, 0, 95}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 7}]] &, {0}, 4] (* Robert G. Wilson v, Jul 27 2006 *)
PROG
(PARI) a(n)=if(n<1, 0, if(n%8, a(n-1)+1, a(n/8)))
(PARI) a(n) = sumdigits(n, 8); \\ Michel Marcus, Jul 10 2022
(Haskell)
a053829 n = q 0 $ divMod n 8 where
q r (0, d) = r + d
q r (m, d) = q (r + d) $ divMod m 8
-- Reinhard Zumkeller, May 15 2011
(Python)
def A053829(n): return sum(int(d) for d in oct(n)[2:]) # Chai Wah Wu, Jul 09 2022
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved