

A053829


Sum of digits of (n written in base 8).


19



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
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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)=n7*(sum(k>0, floor(n/8^k))=n7*A054897(n).  Benoit Cloitre, Dec 19 2002
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


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(n1)+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, A231680A231683.
Cf. A173528.  Omar E. Pol, Feb 21 2010
Sequence in context: A338458 A002376 A055401 * A033928 A194754 A167972
Adjacent sequences: A053826 A053827 A053828 * A053830 A053831 A053832


KEYWORD

base,nonn


AUTHOR

Henry Bottomley, Mar 28 2000


STATUS

approved



