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A053829 Sum of digits of (n written in base 8). 17
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 (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}, 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

a(n) = A138530(n,8) for n > 7. - 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, Digit Sum

Eric Weisstein's World of Mathematics, Octal

FORMULA

a(0)=0, a(8n+i)=a(n)+i 0<=i<=7; a(n)=n-7*(sum(k>0, floor(n/8^k))=n-7*A054897(n). - Benoit Cloitre, Dec 19 2002

a(n)=Sum_k>=0 {A031045(n,k)}. - Philippe Deléham, Oct 21 2011

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)))

(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

CROSSREFS

Cf. A000120, A007953, A231680-A231683.

Cf. A173528. - Omar E. Pol, Feb 21 2010

Sequence in context: A010886 A002376 A055401 * A033928 A194754 A167972

Adjacent sequences:  A053826 A053827 A053828 * A053830 A053831 A053832

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Mar 28 2000

STATUS

approved

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Last modified November 21 12:23 EST 2018. Contains 317449 sequences. (Running on oeis4.)