A053836 Sum of digits of n written in base 16.

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

Offset: 0

Author

Henry Bottomley, Mar 28 2000

Keywords

• base
• nonn
• easy

Comments

a(n) = A138530(n,16) for n > 15. - Reinhard Zumkeller, Mar 26 2008

Examples

			a(20) = 1 + 4 = 5 because 20 is written as "14" in base 16.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Robert Walker, Self Similar Sloth Canon Number Sequences
• Eric Weisstein's World of Mathematics, Hexadecimal
• Eric Weisstein's World of Mathematics, Digit Sum

Crossrefs

Cf. A000120, A007953.

Programs

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
-- Reinhard Zumkeller, May 15 2011

Mathematica

Table[Plus @@ IntegerDigits[n, 16], {n, 0, 150}] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

PARI

a(n)=if(n<1,0,if(n%16,a(n-1)+1,a(n/16)))

PARI

a(n) = sumdigits(n, 16); \\ Michel Marcus, Jan 19 2023

Python

def A053836(n): return sum(int(d,16) for d in hex(n)[2:]) # Chai Wah Wu, Jan 19 2023

Formula

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