A309597 a(n) is the A325907(n)-th triangular number.

6, 666, 5656566, 555665666566566, 5555555666655656666556566566566, 555555555555555666666665555665666666666555566566666556566566566

Offset: 1

Author

Seiichi Manyama, Sep 14 2019

Keywords

• nonn

Comments

a(n) decimal expansion includes A141023(n-1) 5's and A052950(n) 6's in digits.

All terms are elements of A213516.

Examples

			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)
       ------- -------- --------
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A000217, A052950, A093142, A141023, A213516, A325907, A325910, A325493.

Programs

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)

Formula

a(n) = A000217(A325907(n)).

a(n) = A093142(2^n - 1) + A325493(n-1) + A325910(n-1) * 10^(2^(n-1)).