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A053834 Sum of digits of n written in base 14.

%I A053834 #31 Feb 16 2025 08:32:42
%S A053834 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,
%T A053834 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,
%U A053834 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
%N A053834 Sum of digits of n written in base 14.
%H A053834 Tanar Ulric, <a href="/A053834/b053834.txt">Table of n, a(n) for n = 0..10000</a>
%H A053834 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 A053834 Robert Walker, <a href="https://web.archive.org/web/20190411111921/http://robertinventor.com/ftswiki/Self_Similar_Sloth_Canon_Number_Sequences">Self Similar Sloth Canon Number Sequences</a>.
%H A053834 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>.
%F A053834 From _Benoit Cloitre_, Dec 19 2002: (Start)
%F A053834 a(0) = 0, a(14n+i) = a(n)+i for 0 <= i <= 13.
%F A053834 a(n) = n-13*(Sum_{k>0} floor(n/14^k)). (End)
%F A053834 a(n) = A138530(n,14) for n > 13. - _Reinhard Zumkeller_, Mar 26 2008
%F A053834 Sum_{n>=1} a(n)/(n*(n+1)) = 14*log(14)/13 (Shallit, 1984). - _Amiram Eldar_, Jun 03 2021
%e A053834 a(20) = 1 + 6 = 7 because 20 is written as "16" in base 14.
%t A053834 Array[Total[IntegerDigits[#,14]]&,90,0] (* _Harvey P. Dale_, Jul 16 2011 *)
%o A053834 (PARI) a(n)=if(n<1,0,if(n%14,a(n-1)+1,a(n/14)))
%o A053834 (PARI) a(n) = sumdigits(n, 14); \\ _Michel Marcus_, Jun 03 2021
%Y A053834 Cf. A000120, A007953, A138530.
%K A053834 base,nonn
%O A053834 0,3
%A A053834 _Henry Bottomley_, Mar 28 2000