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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.)