The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A053829 Sum of digits of (n written in base 8). 27
 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 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 Cf. A000120, A007953, A231680, A231681, A231682, A231683. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 13:22 EDT 2023. Contains 365579 sequences. (Running on oeis4.)