A327294 a(n) = (A325907(n) + 1) * (10^(2^(n-1)) - A325907(n)).

28, 2368, 22326868, 2222332366866868, 22222222333322326666886866866868, 2222222222222222333333332222332366666666888866866666886866866868

Offset: 1

Author

Seiichi Manyama, Sep 16 2019

Keywords

• nonn

Comments

a(n) is composed of digits {2,3,6,8}.

Examples

			a(1) =                2 * 10^1  +                8.
a(2) =               23 * 10^2  +               68.
a(3) =             2232 * 10^4  +             6868.
a(4) =         22223323 * 10^8  +         66866868.
a(5) = 2222222233332232 * 10^16 + 6666886866866868.
And
                      2 = 2 * (10^1  - 1)/9 +        0.
                     23 = 2 * (10^2  - 1)/9 +        1.
                   2232 = 2 * (10^4  - 1)/9 +       10.
               22223323 = 2 * (10^8  - 1)/9 +     1101.
       2222222233332232 = 2 * (10^16 - 1)/9 + 11110010.
And
                      8 = 8 * (10^1  - 1)/9 - 2 *                0.
                     68 = 8 * (10^2  - 1)/9 - 2 *               10.
                   6868 = 8 * (10^4  - 1)/9 - 2 *             1010.
               66866868 = 8 * (10^8  - 1)/9 - 2 *         11011010.
       6666886866866868 = 8 * (10^16 - 1)/9 - 2 * 1111001011011010.
		

Crossrefs

Cf. A325907, A325910, A325493, A327266.

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 + 1) * (10 ** (2 ** (n - 1)) - b)
end
def A327294(n)
  (1..n).map{|i| A(i)}
end
p A327294(6)

Formula

a(n) = 2 * (10^(2^n) + 3 * 10^(2^(n-1)) - 4)/9 - 2 * A325493(n-1) + A325910(n-1) * 10^(2^(n-1)).