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(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
EXAMPLE
a(20) = 1 + 5 = 6 because 20 is written as "15" in base 15.
MATHEMATICA
a[n_] := Total[IntegerDigits[n, 15]]; Array[a, 100, 0] (* Amiram Eldar, Aug 03 2023 *)
PROG
(PARI) a(n)=if(n<1, 0, if(n%15, a(n-1)+1, a(n/15)))
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Henry Bottomley, Mar 28 2000
STATUS
approved