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A053824
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Sum of digits of n written in base 5.
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13
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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; internal format)
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OFFSET
| 0,3
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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 (reinhard.zumkeller(AT)gmail.com), Mar 26 2008
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LINKS
| Eric Weisstein's World of Mathematics, Digit Sum
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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. [From W. Bomfim webonfim(AT)bol.com Jan 01, 2011]
a(n)=Sum_k>=0 {A031235(n,k)}. - From DELEHAM Philippe, Oct 21 2011.
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EXAMPLE
| a(20)=4+0=4 because 20 is written as 40 base 5
Contribution from Omar E. Pol (info(AT)polprimos.com), 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)
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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]
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PROG
| (PARI) a(n)=if(n<1, 0, if(n%5, a(n-1)+1, a(n/5)))
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CROSSREFS
| Cf. A000120, A007953.
Cf. A173525. [From Omar E. Pol (info(AT)polprimos.com), Feb 21 2010]
Cf. A173670 (last non-zero decimal digit of (10^n)!) [From W. Bomfim webonfim(AT)bol.com Jan 01, 2011]
Sequence in context: A092196 A100878 A145172 * A033925 A064866 A024855
Adjacent sequences: A053821 A053822 A053823 * A053825 A053826 A053827
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KEYWORD
| base,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 28 2000
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