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A053836
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Sum of digits of n written in base 16.
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13
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 5, 6, 7
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OFFSET
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0,3
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Digit Sum
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FORMULA
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a(0)=0, a(16*n+i)=a(n)+i 0<=i<=15; a(n)=n-15*(sum(k>0, floor(n/16^k)). - Benoit Cloitre, Dec 19 2002
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EXAMPLE
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a(20) = 1 + 4 = 5 because 20 is written as "14" in base 16.
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<1, 0, if(n%16, a(n-1)+1, a(n/16)))
(Haskell)
a053836 n = q 0 $ divMod n 16 where
q r (0, d) = r + d
q r (m, d) = q (r + d) $ divMod m 16
(Python)
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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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