A053831 Sum of digits of n written in base 11.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 9, 10, 11, 12, 13, 14, 15

Offset

0,3

Comments

Also the fixed point of the morphism 0->{0,1,2,3,4,5,6,7,8,9,10}, 1->{1,2,3,4,5,6,7,8,9,10,11}, 2->{2,3,4,5,6,7,8,9,10,11,12}, etc. - Robert G. Wilson v, Jul 27 2006

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(11n+i) = a(n)+i for 0 <= i <= 10.

a(n) = n-(m-1)*(Sum_{k>0} floor(n/m^k)) = n-(m-1)*A064458(n). (End)

a(n) = A138530(n,11) for n > 10. - Reinhard Zumkeller, Mar 26 2008

Sum_{n>=1} a(n)/(n*(n+1)) = 11*log(11)/10 (Shallit, 1984). - Amiram Eldar, Jun 03 2021

Example

a(20) = 1 + 9 = 10 because 20 is written as 19 base 11.

Mathematica

Table[Plus @@ IntegerDigits[n, 11], {n, 0, 86}] (* or *)
Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 10}]] &, {0}, 2] (* Robert G. Wilson v, Jul 27 2006 *)

Prog

(PARI) a(n)=if(n<1, 0, if(n%11, a(n-1)+1, a(n/11)))
(PARI) a(n)=sumdigits(n, 11) \\ Charles R Greathouse IV, Oct 20 2021
(C) int Base11DigitSum(int n) {
   int count = 0;
   while (n != 0) { count += n % 11; n = n / 11; }
   return count;
} // Tanar Ulric, Oct 20 2021

Crossrefs

Cf. A007953, A064458, A138530.

Sum of digits of n written in bases 2-16: A000120, A053735, A053737, A053824, A053827, A053828, A053829, A053830, A007953, this sequence, A053832, A053833, A053834, A053835, A053836.

Sequence in context: A214587 A365762 A010889 * A263131 A349315 A274206

Adjacent sequences: A053828 A053829 A053830 * A053832 A053833 A053834

Keyword

base,nonn,easy

Author

Henry Bottomley, Mar 28 2000

Status

approved