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

0,3

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

Cf. A000120, A007953, A138530.

Sequence in context: A080331 A297247 A167463 * A072965 A297248 A043274

Adjacent sequences: A053832 A053833 A053834 * A053836 A053837 A053838

Keyword

base,nonn

Author

Henry Bottomley, Mar 28 2000

Status

approved