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A309597 a(n) is the A325907(n)-th triangular number. 5
6, 666, 5656566, 555665666566566, 5555555666655656666556566566566, 555555555555555666666665555665666666666555566566666556566566566 (list; graph; refs; listen; history; text; internal format)
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

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

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)

CROSSREFS

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

Sequence in context: A220858 A222743 A222720 * A269842 A331724 A046985

Adjacent sequences:  A309594 A309595 A309596 * A309598 A309599 A309600

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 14 2019

STATUS

approved

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Last modified April 5 16:37 EDT 2020. Contains 333245 sequences. (Running on oeis4.)