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%I #52 Feb 12 2023 10:18:59
%S 1,22,333,4444,55555,666666,7777777,88888888,999999999,
%T 10101010101010101010,1111111111111111111111,121212121212121212121212,
%U 13131313131313131313131313,1414141414141414141414141414,151515151515151515151515151515,16161616161616161616161616161616
%N Concatenate n n times.
%D F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.
%H Reinhard Zumkeller, <a href="/A000461/b000461.txt">Table of n, a(n) for n = 1..333</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>
%F 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
%F A055642(a(n)) = n * A055642(n). - _Reinhard Zumkeller_, Apr 26 2011
%F a(n) = Sum_{i=0..n-1} (n*10^(i*(floor(log(10, n)) + 1))). - _José de Jesús Camacho Medina_, Dec 10 2014
%e From _Bruno Berselli_, Oct 05 2018: (Start)
%e . 1 * 9 = 09
%e . 22 * 9 = 198
%e . 333 * 9 = 2997
%e . 4444 * 9 = 39996
%e . 55555 * 9 = 499995
%e . 666666 * 9 = 5999994
%e . 7777777 * 9 = 69999993
%e . 88888888 * 9 = 799999992
%e . 999999999 * 9 = 8999999991
%e (End)
%p a:= n-> parse(cat(n$n)):
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Apr 26 2011
%t 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 *)
%t Table[FromDigits[Flatten[IntegerDigits/@Table[n,{n}]]],{n,15}] (* _Harvey P. Dale_, Mar 01 2015 *)
%t Table[FromDigits[PadRight[{},n IntegerLength[n],IntegerDigits[n]]],{n,15}] (* _Harvey P. Dale_, Jun 19 2016 *)
%o (Haskell)
%o a000461 n = (read $ concat $ replicate n $ show n) :: Integer
%o -- _Reinhard Zumkeller_, Apr 26 2011
%o (PARI) a(n) = eval(concat(apply(x->Str(x), vector(n, k, n)))); \\ _Michel Marcus_, Oct 05 2018; Feb 12 2023
%o (Python)
%o def a(n): return int(str(n)*n)
%o print([a(n) for n in range(1, 17)]) # _Michael S. Branicky_, Jan 22 2021
%Y Cf. A048376, A053422.
%K nonn,base,easy
%O 1,2
%A John Radu (Suttones(AT)aol.com)
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