login
A327294
a(n) = (A325907(n) + 1) * (10^(2^(n-1)) - A325907(n)).
2
28, 2368, 22326868, 2222332366866868, 22222222333322326666886866866868, 2222222222222222333333332222332366666666888866866666886866866868
OFFSET
1,1
COMMENTS
a(n) is composed of digits {2,3,6,8}.
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)).
EXAMPLE
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.
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 + 1) * (10 ** (2 ** (n - 1)) - b)
end
def A327294(n)
(1..n).map{|i| A(i)}
end
p A327294(6)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 16 2019
STATUS
approved