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 A053824 Sum of digits of (n written in base 5). 30
 0, 1, 2, 3, 4, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 6, 7, 8, 9, 10, 7, 8, 9, 10, 11, 4, 5, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the fixed point of the morphism 0->{0,1,2,3,4}, 1->{1,2,3,4,5}, 2->{2,3,4,5,6}, etc. - Robert G. Wilson v, Jul 27 2006 a(n) = A138530(n,5) for n > 4. - Reinhard Zumkeller, Mar 26 2008 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..3125=5^5 Robert Walker, Self Similar Sloth Canon Number Sequences Eric Weisstein's World of Mathematics, Digit Sum FORMULA From Benoit Cloitre, Dec 19 2002: (Start) a(0)=0, a(5n+i) = a(n) + i, 0 <= i <= 4; a(n) = n - 4*Sum_{k>=1} floor(n/5^k) = n - 4*A027868(n). (End) If i >= 2, a(2^i) mod 4 = 0. - Washington Bomfim, Jan 01 2011 a(n) = Sum_{k>=0} A031235(n,k). - Philippe Deléham, Oct 21 2011 a(0) = 0; a(n) = a(n - 5^floor(log_5(n))) + 1. - Ilya Gutkovskiy, Aug 23 2019 EXAMPLE a(20) = 4 + 0 = 4 because 20 is written as 40 in base 5. From Omar E. Pol, Feb 21 2010: (Start) It appears that this can be written as a triangle (see the conjecture in the entry A000120): 0, 1,2,3,4, 1,2,3,4,5,2,3,4,5,6,3,4,5,6,7,4,5,6,7,8, 1,2,3,4,5,2,3,4,5,6,3,4,5,6,7,4,5,6,7,8,5,6,7,8,9,2,3,4,5,6,3,4,5,6,7,4,5,... (End) MATHEMATICA Table[Plus @@ IntegerDigits[n, 5], {n, 0, 100}] (* or *) Nest[Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 4}]] &, {0}, 4] (* Robert G. Wilson v, Jul 27 2006 *) f[n_] := n - 4 Sum[Floor[n/5^k], {k, n}]; Array[f, 103, 0] PROG (PARI) a(n)=if(n<1, 0, if(n%5, a(n-1)+1, a(n/5))) (PARI) a(n) = sumdigits(n, 5); \\ Michel Marcus, Aug 24 2019 (Haskell) a053824 0 = 0 a053824 x = a053824 x' + d  where (x', d) = divMod x 5 -- Reinhard Zumkeller, Jan 31 2014 (MAGMA) [&+Intseq(n, 5):n in [0..100]]; // Marius A. Burtea, Aug 24 2019 CROSSREFS Cf. A000120, A007953, A053735, A053737, A053827, A231668-A231671. Cf. A173525. - Omar E. Pol, Feb 21 2010 Cf. A173670 (last nonzero decimal digit of (10^n)!). - Washington Bomfim, Jan 01 2011 Sequence in context: A338493 A280053 A283365 * A033925 A064866 A024855 Adjacent sequences:  A053821 A053822 A053823 * A053825 A053826 A053827 KEYWORD base,nonn,look AUTHOR Henry Bottomley, Mar 28 2000 STATUS approved

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Last modified April 13 11:56 EDT 2021. Contains 342936 sequences. (Running on oeis4.)