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A000461
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Concatenate n n times.
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25
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1, 22, 333, 4444, 55555, 666666, 7777777, 88888888, 999999999, 10101010101010101010, 1111111111111111111111, 121212121212121212121212, 13131313131313131313131313, 1414141414141414141414141414, 151515151515151515151515151515, 16161616161616161616161616161616
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..333
Eric Weisstein's World of Mathematics, Smarandache Sequences
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FORMULA
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a(n) = n*(10^(n*L(n))-1)/(10^L(n)-1) where L(n) = A004216(n)+1 = floor(log_10(10n)). - Henry Bottomley, Jun 01 2000
A055642(a(n)) = n * A055642(n). - Reinhard Zumkeller, Apr 26 2011
a(n) = Sum_{i=0..n-1} (n*10^(i*(floor(log(10, n)) + 1))). - José de Jesús Camacho Medina, Dec 10 2014
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EXAMPLE
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From Bruno Berselli, Oct 05 2018: (Start)
. 1 * 9 = 09
. 22 * 9 = 198
. 333 * 9 = 2997
. 4444 * 9 = 39996
. 55555 * 9 = 499995
. 666666 * 9 = 5999994
. 7777777 * 9 = 69999993
. 88888888 * 9 = 799999992
. 999999999 * 9 = 8999999991
(End)
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MAPLE
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a:= n-> parse(cat(n$n)):
seq(a(n), n=1..20); # Alois P. Heinz, Apr 26 2011
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MATHEMATICA
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Table[Sum[(n)*10^(i*(Floor[Log[10, n]] + 1)), {i, 0, n - 1}], {n, 1, 30}] (* José de Jesús Camacho Medina, Dec 10 2014 *)
Table[FromDigits[Flatten[IntegerDigits/@Table[n, {n}]]], {n, 15}] (* Harvey P. Dale, Mar 01 2015 *)
Table[FromDigits[PadRight[{}, n IntegerLength[n], IntegerDigits[n]]], {n, 15}] (* Harvey P. Dale, Jun 19 2016 *)
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PROG
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(Haskell)
a000461 n = (read $ concat $ replicate n $ show n) :: Integer
-- Reinhard Zumkeller, Apr 26 2011
(PARI) a(n) = eval(concat(apply(x->Str(x), vector(n, k, n)))); \\ Michel Marcus, Oct 05 2018; Feb 12 2023
(Python)
def a(n): return int(str(n)*n)
print([a(n) for n in range(1, 17)]) # Michael S. Branicky, Jan 22 2021
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CROSSREFS
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Cf. A048376, A053422.
Sequence in context: A158849 A048376 A053422 * A216730 A048795 A068186
Adjacent sequences: A000458 A000459 A000460 * A000462 A000463 A000464
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KEYWORD
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nonn,base,easy
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AUTHOR
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John Radu (Suttones(AT)aol.com)
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STATUS
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approved
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