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

0,3

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(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

Example

a(20) = 1 + 6 = 7 because 20 is written as "16" in base 14.

Mathematica

Array[Total[IntegerDigits[#, 14]]&, 90, 0] (* Harvey P. Dale, Jul 16 2011 *)

Prog

(PARI) a(n)=if(n<1, 0, if(n%14, a(n-1)+1, a(n/14)))
(PARI) a(n) = sumdigits(n, 14); \\ Michel Marcus, Jun 03 2021

Crossrefs

Cf. A000120, A007953, A138530.

Sequence in context: A071523 A297244 A070696 * A297245 A043273 A268982

Adjacent sequences: A053831 A053832 A053833 * A053835 A053836 A053837

Keyword

base,nonn

Author

Henry Bottomley, Mar 28 2000

Status

approved