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A053829
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Sum of digits of n written in base 8.
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6
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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; internal format)
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OFFSET
| 0,3
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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 (reinhard.zumkeller(AT)gmail.com), Mar 26 2008
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Digit Sum
Eric Weisstein's World of Mathematics, Octal
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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)}. - From DELEHAM Philippe, Oct 21 2011.
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EXAMPLE
| a(20)=2+4=6 because 20 is written as 24 base 8
Contribution from Omar E. Pol (info(AT)polprimos.com), 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)
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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 *)
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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
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CROSSREFS
| Cf. A000120, A007953.
Cf. A173528. [From Omar E. Pol (info(AT)polprimos.com), Feb 21 2010]
Sequence in context: A010886 A002376 A055401 * A033928 A194754 A167972
Adjacent sequences: A053826 A053827 A053828 * A053830 A053831 A053832
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KEYWORD
| base,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000
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