A327294 - OEIS

%I #36 Sep 21 2019 14:39:34

%S 28,2368,22326868,2222332366866868,22222222333322326666886866866868,

%T 2222222222222222333333332222332366666666888866866666886866866868

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

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

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

%e a(1) =                2 * 10^1  +                8.

%e a(2) =               23 * 10^2  +               68.

%e a(3) =             2232 * 10^4  +             6868.

%e a(4) =         22223323 * 10^8  +         66866868.

%e a(5) = 2222222233332232 * 10^16 + 6666886866866868.

%e And

%e                       2 = 2 * (10^1  - 1)/9 +        0.

%e                      23 = 2 * (10^2  - 1)/9 +        1.

%e                    2232 = 2 * (10^4  - 1)/9 +       10.

%e                22223323 = 2 * (10^8  - 1)/9 +     1101.

%e        2222222233332232 = 2 * (10^16 - 1)/9 + 11110010.

%e And

%e                       8 = 8 * (10^1  - 1)/9 - 2 *                0.

%e                      68 = 8 * (10^2  - 1)/9 - 2 *               10.

%e                    6868 = 8 * (10^4  - 1)/9 - 2 *             1010.

%e                66866868 = 8 * (10^8  - 1)/9 - 2 *         11011010.

%e        6666886866866868 = 8 * (10^16 - 1)/9 - 2 * 1111001011011010.

%o (Ruby)

%o def A(n)

%o   a = [3, 6]

%o   b = ([[3]] + (1..n - 1).map{|i| [a[i % 2]] * (2 ** (i - 1))}).reverse.join.to_i

%o   (b + 1) * (10 ** (2 ** (n - 1)) - b)

%o end

%o def A327294(n)

%o   (1..n).map{|i| A(i)}

%o end

%o p A327294(6)

%Y Cf. A325907, A325910, A325493, A327266.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Sep 16 2019