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A053827
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Sum of digits of n written in base 6.
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6
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0, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 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}, 1->{1,2,3,4,5,6}, 2->{2,3,4,5,6,7}, etc. - Robert G. Wilson v Jul 27 2006.
a(n) = A138530(n,6) for n > 5. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 26 2008
Sum of six consecutive terms is (15,21,27,33,39,45; 21,27,33,39,45,51; 27,33,39,45,51,57; and so on) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 02 2010]
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LINKS
| Eric Weisstein's World of Mathematics, Digit Sum
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FORMULA
| a(0)=0, a(6n+i)=a(n)+i 0<=i<=5; a(n)=n-5*(sum(k>0, floor(n/6^k))=n-5*A054895(n). - Benoit Cloitre, Dec 19, 2002
a(n)=Sumk>=0 {A030567(n,k)}. - From DELEHAM Philippe, Oct 21 2011.
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EXAMPLE
| a(20)=3+2=5 because 20 is written as 32 base 6
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,
1,2,3,4,5,6,2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,
1,2,3,4,5,6,2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,2...
where the rows converge to A173526.
(End)
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MATHEMATICA
| Table[Plus @@ IntegerDigits[n, 6], {n, 0, 100}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 5}]] &, {0}, 4] (* Robert G. Wilson v Jul 27 2006 *)
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PROG
| (PARI) a(n)=if(n<1, 0, if(n%6, a(n-1)+1, a(n/6)))
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CROSSREFS
| Cf. A000120, A007953.
Cf. A173526. [From Omar E. Pol (info(AT)polprimos.com), Feb 21 2010]
Sequence in context: A105932 A106652 A193106 * A033926 A193042 A050269
Adjacent sequences: A053824 A053825 A053826 * A053828 A053829 A053830
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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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