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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 January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)