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A053834
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Sum of digits of n written in base 14.
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9
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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
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OFFSET
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0,3
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LINKS
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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.
Eric Weisstein's World of Mathematics, Digit Sum.
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FORMULA
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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)
Sum_{n>=1} a(n)/(n*(n+1)) = 14*log(14)/13 (Shallit, 1984). - Amiram Eldar, Jun 03 2021
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EXAMPLE
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a(20) = 1 + 6 = 7 because 20 is written as "16" in base 14.
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MATHEMATICA
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Array[Total[IntegerDigits[#, 14]]&, 90, 0] (* Harvey P. Dale, Jul 16 2011 *)
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PROG
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(PARI) a(n)=if(n<1, 0, if(n%14, a(n-1)+1, a(n/14)))
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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