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A309597
a(n) is the A325907(n)-th triangular number.
5
6, 666, 5656566, 555665666566566, 5555555666655656666556566566566, 555555555555555666666665555665666666666555566566666556566566566
OFFSET
1,1
COMMENTS
a(n) decimal expansion includes A141023(n-1) 5's and A052950(n) 6's in digits.
All terms are elements of A213516.
LINKS
FORMULA
a(n) = A000217(A325907(n)).
a(n) = A093142(2^n - 1) + A325493(n-1) + A325910(n-1) * 10^(2^(n-1)).
EXAMPLE
a(1) = 6 = 6 + 0 + 0 * 10^1.
a(2) = 666 = 556 + 10 + 1 * 10^2.
a(3) = 5656566 = 5555556 + 1010 + 10 * 10^4.
a(4) = 555665666566566 = 555555555555556 + 11011010 + 1101 * 10^8.
------------------------------------------------------------------
a(2) = 6 6 6. ( 3 6's)
- -
a(3) = 5 65 65 66. ( 3 5's and 4 6's)
- -- --
a(4) = 555 6656 6656 6566. ( 6 5's and 9 6's)
--- ---- ----
a(5) = 5555555 66665565 66665565 66566566. (15 5's and 16 6's)
------- -------- --------
PROG
(Ruby)
def A325907(n)
a = [3]
(2..n).each{|i|
j = 10 ** (2 ** (i - 2))
a << (j + 3) * (j - 1) / 3 - a[-1]
}
a
end
def A309597(n)
A325907(n).map{|i| i * (i + 1) / 2}
end
p A309597(10)
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 14 2019
STATUS
approved