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A053824 Sum of digits of (n written in base 5). 27
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

a(0)=0, a(5n+i)=a(n)+i 0<=i<=4; a(n)=n-4*(sum(k>0, floor(n/5^k))=n-4*A027868(n). - Benoit Cloitre, Dec 19 2002

From the second formula, a(n)=n-4*(sum(k>0, floor(n/5^k)). Also, 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

EXAMPLE

a(20) = 4 + 0 = 4 because 20 is written as 40 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)))

(Haskell)

a053824 0 = 0

a053824 x = a053824 x' + d  where (x', d) = divMod x 5

-- Reinhard Zumkeller, Jan 31 2014

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: 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

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Last modified July 27 04:53 EDT 2017. Contains 289841 sequences.