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
Examples
a(20) = 1 + 7 = 8 because 20 is written as "17" in base 13.
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.
Programs
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Mathematica
Total[IntegerDigits[#,13]]&/@Range[0,90] (* Harvey P. Dale, Jul 17 2012 *)
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PARI
a(n)=if(n<1,0,if(n%13,a(n-1)+1,a(n/13)))
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