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%I #30 Jan 19 2023 02:14:52
%S 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,
%T 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,
%U 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
%N Sum of digits of n written in base 16.
%C a(n) = A138530(n,16) for n > 15. - _Reinhard Zumkeller_, Mar 26 2008
%H Reinhard Zumkeller, <a href="/A053836/b053836.txt">Table of n, a(n) for n = 0..10000</a>
%H Robert Walker, <a href="http://robertinventor.com/ftswiki/Self_Similar_Sloth_Canon_Number_Sequences">Self Similar Sloth Canon Number Sequences</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hexadecimal.html">Hexadecimal</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DigitSum.html">Digit Sum</a>
%F 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
%e a(20) = 1 + 4 = 5 because 20 is written as "14" in base 16.
%t Table[Plus @@ IntegerDigits[n, 16], {n, 0, 150}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%o (PARI) a(n)=if(n<1,0,if(n%16,a(n-1)+1,a(n/16)))
%o (PARI) a(n) = sumdigits(n, 16); \\ _Michel Marcus_, Jan 19 2023
%o (Haskell)
%o a053836 n = q 0 $ divMod n 16 where
%o q r (0, d) = r + d
%o q r (m, d) = q (r + d) $ divMod m 16
%o -- _Reinhard Zumkeller_, May 15 2011
%o (Python)
%o def A053836(n): return sum(int(d,16) for d in hex(n)[2:]) # _Chai Wah Wu_, Jan 19 2023
%Y Cf. A000120, A007953.
%K base,nonn
%O 0,3
%A _Henry Bottomley_, Mar 28 2000
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