A000461 Concatenate n n times.

1, 22, 333, 4444, 55555, 666666, 7777777, 88888888, 999999999, 10101010101010101010, 1111111111111111111111, 121212121212121212121212, 13131313131313131313131313, 1414141414141414141414141414, 151515151515151515151515151515, 16161616161616161616161616161616

Offset: 1

Author

John Radu (Suttones(AT)aol.com)

Keywords

• nonn
• base
• easy

Examples

			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)
		

References

• F. Smarandache, "Properties of the numbers", Univ. of Craiova Archives, 1975; Arizona State University Special Collections, Tempe, AZ.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..333
• Eric Weisstein's World of Mathematics, Smarandache Sequences

Crossrefs

Cf. A048376, A053422.

Programs

Haskell

a000461 n = (read $ concat $ replicate n $ show n) :: Integer
-- Reinhard Zumkeller, Apr 26 2011

Maple

a:= n-> parse(cat(n$n)):
seq(a(n), n=1..20);  # Alois P. Heinz, Apr 26 2011

Mathematica

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 *)

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

Formula

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