A053834 Sum of digits of n written in base 14.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Offset: 0
Examples
a(20) = 1 + 6 = 7 because 20 is written as "16" in base 14.
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
Array[Total[IntegerDigits[#,14]]&,90,0] (* Harvey P. Dale, Jul 16 2011 *)
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PARI
a(n)=if(n<1,0,if(n%14,a(n-1)+1,a(n/14)))
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PARI
a(n) = sumdigits(n, 14); \\ Michel Marcus, Jun 03 2021
Formula
From Benoit Cloitre, Dec 19 2002: (Start)
a(0) = 0, a(14n+i) = a(n)+i for 0 <= i <= 13.
a(n) = n-13*(Sum_{k>0} floor(n/14^k)). (End)
a(n) = A138530(n,14) for n > 13. - Reinhard Zumkeller, Mar 26 2008
Sum_{n>=1} a(n)/(n*(n+1)) = 14*log(14)/13 (Shallit, 1984). - Amiram Eldar, Jun 03 2021