A300517 a(n) is the concatenation of n n times, n-1 n-1 times, ..., 22, 1.

1, 221, 333221, 4444333221, 555554444333221, 666666555554444333221, 7777777666666555554444333221, 888888887777777666666555554444333221, 999999999888888887777777666666555554444333221, 10101010101010101010999999999888888887777777666666555554444333221

Offset: 1

Author

Seiichi Manyama, Mar 07 2018

Keywords

• nonn
• base

Comments

a(n) is composite for all 2 <= n <= 1000. - David Cleaver, Apr 14 2023

Examples

			a(4) = 4444333221 because 4 concatenated four times then concatenated with 3 three times and 2 twice and 1 once gives 4444333221.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..31

Crossrefs

Cf. A000461, A098129, A361751 (number of decimal digits).

Programs

Maple

a:= n-> parse(cat(seq((n-i)$(n-i), i=0..n-1))):
seq(a(n), n=1..12);  # Alois P. Heinz, Mar 07 2018

PARI

a(n) = {my(a=0, b=0, d=1, i);
  for(i=1, n, b = logint(i, 10)+1;
    a += d*i*(10^(i*b)-1)/(10^b-1);
    d *= 10^(i*b); ); return(a); } \\ David Cleaver, Apr 14 2023

Ruby

def A300517(n)
  a = '1'
  [1] + (2..n).map{|i| a = (i.to_s * i + a.to_s).to_i}
end
p A300517(20)