

A053824


Sum of digits of (n written in base 5).


28



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
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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(n1)+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, A231668A231671.
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: A145172 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



