A053833 Sum of digits of n written in base 13.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 6, 7, 8, 9, 10, 11, 12

Offset

0,3

Links

Tanar Ulric, 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. 59-60; Two series, solution to Problem 6450, ibid., Vol. 92, No. 7 (1985), pp. 513-514.

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(13n+i) = a(n)+i for 0 <= i <= 12.

a(n) = n-12*(Sum_{k>0} floor(n/13^k)). (End)

a(n) = A138530(n,13) for n > 12. - Reinhard Zumkeller, Mar 26 2008

Sum_{n>=1} a(n)/(n*(n+1)) = 13*log(13)/12 (Shallit, 1984). - Amiram Eldar, Jun 03 2021

Example

a(20) = 1 + 7 = 8 because 20 is written as "17" in base 13.

Mathematica

Total[IntegerDigits[#, 13]]&/@Range[0, 90]  (* Harvey P. Dale, Jul 17 2012 *)

Prog

(PARI) a(n)=if(n<1, 0, if(n%13, a(n-1)+1, a(n/13)))

Crossrefs

Cf. A000120, A007953, A138530.

Sequence in context: A178787 A297241 A034326 * A167973 A087999 A106614

Adjacent sequences: A053830 A053831 A053832 * A053834 A053835 A053836

Keyword

base,nonn

Author

Henry Bottomley, Mar 28 2000

Status

approved