login
A327266
Product of A325907(n) and its 9's complement.
2
18, 2268, 22316868, 2222332266866868, 22222222333322316666886866866868, 2222222222222222333333332222332266666666888866866666886866866868
OFFSET
1,1
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)).
EXAMPLE
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.
PROG
(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)
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 15 2019
STATUS
approved