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A053827 Sum of digits of (n written in base 6). 17
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; text; internal format)
OFFSET

0,3

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, 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). - Vincenzo Librandi, Aug 02 2010

LINKS

Indranil Ghosh, 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

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)=Sum_{k>=0} A030567(n,k). - Philippe Deléham, Oct 21 2011

EXAMPLE

a(20)=3+2=5 because 20 is written as 32 base 6

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,

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)

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 *)

PROG

(PARI) a(n)=if(n<1, 0, if(n%6, a(n-1)+1, a(n/6)))

CROSSREFS

Cf. A000120, A007953, A053735, A053737, A053824, A231672-A231675.

Cf. A173526. - Omar E. Pol, Feb 21 2010

Sequence in context: A106652 A193106 A283370 * A033926 A193042 A279478

Adjacent sequences:  A053824 A053825 A053826 * A053828 A053829 A053830

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Mar 28 2000

STATUS

approved

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Last modified October 16 15:20 EDT 2018. Contains 316263 sequences. (Running on oeis4.)