A000461 - OEIS

%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)