

A053827


Sum of digits of (n written in base 6).


26



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
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
Jeffrey O. Shallit, Problem 6450, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 5960; Two series, solution to Problem 6450, ibid., Vol. 92, No. 7 (1985), pp. 513514.
Robert Walker, Self Similar Sloth Canon Number Sequences.
Eric Weisstein's World of Mathematics, Digit Sum.


FORMULA

From Benoit Cloitre, Dec 19 2002: (Start)
a(0) = 0, a(6n+i) = a(n)+i for 0 <= i <= 5.
a(n) = n5*(Sum_{k>0} floor(n/6^k)) = n5*A054895(n). (End)
a(n) = A138530(n,6) for n > 5.  Reinhard Zumkeller, Mar 26 2008
a(n) = Sum_{k>=0} A030567(n,k).  Philippe Deléham, Oct 21 2011
a(0) = 0; a(n) = a(n  6^floor(log_6(n))) + 1.  Ilya Gutkovskiy, Aug 23 2019
Sum_{n>=1} a(n)/(n*(n+1)) = 6*log(6)/5 (Shallit, 1984).  Amiram Eldar, Jun 03 2021


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 :
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.
See the conjecture in the entry A000120. (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)))
(PARI) a(n) = sumdigits(n, 6); \\ Michel Marcus, Aug 24 2019
(Magma) [&+Intseq(n, 6):n in [0..105]]; // Marius A. Burtea, Aug 24 2019


CROSSREFS

Cf. A231672, A231673, A231674, A231675, A138530.
Sum of digits of n written in bases 216: A000120, A053735, A053737, A053824, this sequence, A053828, A053829, A053830, A007953, A053831, A053832, A053833, A053834, A053835, A053836.
Cf. A173526.  Omar E. Pol, Feb 21 2010
Sequence in context: A338491 A338494 A283370 * A033926 A193042 A327463
Adjacent sequences: A053824 A053825 A053826 * A053828 A053829 A053830


KEYWORD

base,nonn


AUTHOR

Henry Bottomley, Mar 28 2000


STATUS

approved



