cp's OEIS Frontend

A000461 Concatenate n n times.

%I A000461 #53 Feb 16 2025 08:32:21
%S A000461 1,22,333,4444,55555,666666,7777777,88888888,999999999,
%T A000461 10101010101010101010,1111111111111111111111,121212121212121212121212,
%U A000461 13131313131313131313131313,1414141414141414141414141414,151515151515151515151515151515,16161616161616161616161616161616
%N A000461 Concatenate n n times.
%D A000461 F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.
%H A000461 Reinhard Zumkeller, <a href="/A000461/b000461.txt">Table of n, a(n) for n = 1..333</a>
%H A000461 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>
%F A000461 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 A000461 A055642(a(n)) = n * A055642(n). - _Reinhard Zumkeller_, Apr 26 2011
%F A000461 a(n) = Sum_{i=0..n-1} (n*10^(i*(floor(log(10, n)) + 1))). - _José de Jesús Camacho Medina_, Dec 10 2014
%e A000461 From _Bruno Berselli_, Oct 05 2018: (Start)
%e A000461 .         1 * 9 = 09
%e A000461 .        22 * 9 = 198
%e A000461 .       333 * 9 = 2997
%e A000461 .      4444 * 9 = 39996
%e A000461 .     55555 * 9 = 499995
%e A000461 .    666666 * 9 = 5999994
%e A000461 .   7777777 * 9 = 69999993
%e A000461 .  88888888 * 9 = 799999992
%e A000461 . 999999999 * 9 = 8999999991
%e A000461 (End)
%p A000461 a:= n-> parse(cat(n$n)):
%p A000461 seq(a(n), n=1..20);  # _Alois P. Heinz_, Apr 26 2011
%t A000461 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 A000461 Table[FromDigits[Flatten[IntegerDigits/@Table[n,{n}]]],{n,15}] (* _Harvey P. Dale_, Mar 01 2015 *)
%t A000461 Table[FromDigits[PadRight[{},n IntegerLength[n],IntegerDigits[n]]],{n,15}] (* _Harvey P. Dale_, Jun 19 2016 *)
%o A000461 (Haskell)
%o A000461 a000461 n = (read $ concat $ replicate n $ show n) :: Integer
%o A000461 -- _Reinhard Zumkeller_, Apr 26 2011
%o A000461 (PARI) a(n) = eval(concat(apply(x->Str(x), vector(n, k, n)))); \\ _Michel Marcus_, Oct 05 2018; Feb 12 2023
%o A000461 (Python)
%o A000461 def a(n): return int(str(n)*n)
%o A000461 print([a(n) for n in range(1, 17)]) # _Michael S. Branicky_, Jan 22 2021
%Y A000461 Cf. A048376, A053422.
%K A000461 nonn,base,easy
%O A000461 1,2
%A A000461 John Radu (Suttones(AT)aol.com)