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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 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 October 20 18:08 EDT 2018. Contains 316401 sequences. (Running on oeis4.)