A053835 Sum of digits of n written in base 15.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 5, 6, 7, 8, 9, 10, 11, 12, 13
Offset: 0
Examples
a(20) = 1 + 5 = 6 because 20 is written as "15" in base 15.
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
a[n_] := Total[IntegerDigits[n, 15]]; Array[a, 100, 0] (* Amiram Eldar, Aug 03 2023 *)
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PARI
a(n)=if(n<1,0,if(n%15,a(n-1)+1,a(n/15)))
Formula
From Benoit Cloitre, Dec 19 2002: (Start)
a(0) = 0, a(15n+i) = a(n)+i, 0<=i<=14.
a(n) = n - 14*(Sum_{k>0} floor(n/15^k)). (End)
a(n) = A138530(n,15) for n > 14. - Reinhard Zumkeller, Mar 26 2008
Sum_{n>=1} a(n)/(n*(n+1)) = 15*log(15)/14 (Shallit, 1984). - Amiram Eldar, Aug 03 2023