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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 (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
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
Jeffrey O. Shallit, Problem 6450, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 59-60; Two series, solution to Problem 6450, ibid., Vol. 92, No. 7 (1985), pp. 513-514.
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) = n-5*(Sum_{k>0} floor(n/6^k)) = n-5*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(n-1)+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
Sum of digits of n written in bases 2-16: 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
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved

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Last modified March 19 06:17 EDT 2024. Contains 370952 sequences. (Running on oeis4.)