A327266 Product of A325907(n) and its 9's complement.

18, 2268, 22316868, 2222332266866868, 22222222333322316666886866866868, 2222222222222222333333332222332266666666888866866666886866866868

Offset: 1

Author

Seiichi Manyama, Sep 15 2019

Keywords

• nonn

Examples

			a(1) =        3 *        6 =         18.
a(2) =       63 *       36 =        2268.
a(3) =     3363 *     6636 =      22316868.
a(4) = 66663363 * 33336636 =  2222332266866868.
-----------------------------------------------
a(1) =        18        =        18        - 2 *        0 +    0 * 10^1.
a(2) =       2268       =       2188       - 2 *       10 +    1 * 10^2.
a(3) =     22316868     =     22218888     - 2 *     1010 +   10 * 10^4.
a(4) = 2222332266866868 = 2222222188888888 - 2 * 11011010 + 1101 * 10^8.
		

Crossrefs

Cf. A002283, A084021, A178630, A325907, A325910, A325493, A327294.

Programs

Ruby

def A(n)
  a = [3, 6]
  b = ([[3]] + (1..n - 1).map{|i| [a[i % 2]] * (2 ** (i - 1))}).reverse.join.to_i
  b * (10 ** (2 ** (n - 1)) - 1 - b)
end
def A327266(n)
  (1..n).map{|i| A(i)}
end
p A327266(6)

Formula

a(n) = A084021(A325907(n)) = A325907(n) * (A002283(2^(n-1)) - A325907(n)).

a(n) = A327294(n) - 10^(2^(n-1)) = a(n) = (2 * 10^(2^n) - 3 * 10^(2^(n-1)) - 8)/9 - 2 * A325493(n-1) + A325910(n-1) * 10^(2^(n-1)).