cp's OEIS Frontend

A053831 Sum of digits of n written in base 11.

%I A053831 #36 Feb 16 2025 08:32:42
%S A053831 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,
%T A053831 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,
%U A053831 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
%N A053831 Sum of digits of n written in base 11.
%C A053831 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
%H A053831 Tanar Ulric, <a href="/A053831/b053831.txt">Table of n, a(n) for n = 0..10000</a>
%H A053831 Jeffrey O. Shallit, <a href="http://www.jstor.org/stable/2322179">Problem 6450</a>, Advanced Problems, The American Mathematical Monthly, Vol. 91, No. 1 (1984), pp. 59-60; <a href="http://www.jstor.org/stable/2322523">Two series, solution to Problem 6450</a>, ibid., Vol. 92, No. 7 (1985), pp. 513-514.
%H A053831 Robert Walker, <a href="http://robertinventor.com/ftswiki/Self_Similar_Sloth_Canon_Number_Sequences">Self Similar Sloth Canon Number Sequences</a>.
%H A053831 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>.
%F A053831 From _Benoit Cloitre_, Dec 19 2002: (Start)
%F A053831 a(0)=0, a(11n+i) = a(n)+i for 0 <= i <= 10.
%F A053831 a(n) = n-(m-1)*(Sum_{k>0} floor(n/m^k)) = n-(m-1)*A064458(n). (End)
%F A053831 a(n) = A138530(n,11) for n > 10. - _Reinhard Zumkeller_, Mar 26 2008
%F A053831 Sum_{n>=1} a(n)/(n*(n+1)) = 11*log(11)/10 (Shallit, 1984). - _Amiram Eldar_, Jun 03 2021
%e A053831 a(20) = 1 + 9 = 10 because 20 is written as 19 base 11.
%t A053831 Table[Plus @@ IntegerDigits[n, 11], {n, 0, 86}] (* or *)
%t A053831 Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 10}]] &, {0}, 2] (* _Robert G. Wilson v_, Jul 27 2006 *)
%o A053831 (PARI) a(n)=if(n<1,0,if(n%11,a(n-1)+1,a(n/11)))
%o A053831 (PARI) a(n)=sumdigits(n,11) \\ _Charles R Greathouse IV_, Oct 20 2021
%o A053831 (C) int Base11DigitSum(int n) {
%o A053831    int count = 0;
%o A053831    while (n != 0) { count += n % 11; n = n / 11; }
%o A053831    return count;
%o A053831 } // _Tanar Ulric_, Oct 20 2021
%Y A053831 Cf. A007953, A064458, A138530.
%Y A053831 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.
%K A053831 base,nonn,easy
%O A053831 0,3
%A A053831 _Henry Bottomley_, Mar 28 2000