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A053833 Sum of digits of n written in base 13. 4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 6, 7, 8, 9, 10, 11, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A138530(n,13) for n > 12. - Reinhard Zumkeller, Mar 26 2008

LINKS

Table of n, a(n) for n=0..84.

Robert Walker, Self Similar Sloth Canon Number Sequences

Eric Weisstein's World of Mathematics, Digit Sum

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).

FORMULA

a(0)=0, a(13n+i)=a(n)+i 0<=i<=12; a(n)=n-12*(sum(k>0, floor(n/13^k)). - Benoit Cloitre, Dec 19 2002

a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=6, a(7)=7, a(8)=8, a(9)=9, a(10)=10, a(11)=11, a(12)=12, a(13)=1, a(n) = a(n-1) + a(n-13) - a(n-14). - Harvey P. Dale, Jul 17 2012

EXAMPLE

a(20) = 1 + 7 = 8 because 20 is written as "17" in base 13.

MATHEMATICA

Total[IntegerDigits[#, 13]]&/@Range[0, 90] (* or *) LinearRecurrence[ {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1}, 90] (* Harvey P. Dale, Jul 17 2012 *)

PROG

(PARI) a(n)=if(n<1, 0, if(n%13, a(n-1)+1, a(n/13)))

CROSSREFS

Cf. A000120, A007953.

Sequence in context: A178787 A297241 A034326 * A167973 A087999 A106614

Adjacent sequences:  A053830 A053831 A053832 * A053834 A053835 A053836

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Mar 28 2000

STATUS

approved

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Last modified June 19 08:41 EDT 2018. Contains 305581 sequences. (Running on oeis4.)