

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
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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)=n5*(sum(k>0, floor(n/6^k))=n5*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(n1)+1, a(n/6)))


CROSSREFS

Cf. A000120, A007953, A053735, A053737, A053824, A231672A231675.
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



