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%I #28 Mar 14 2020 07:02:33
%S 0,1,5,3,4,8,6,16,11,9,10,14,12,13,17,15,25,20,18,19,23,21,22,26,51,
%T 34,29,27,28,32,30,31,35,33,43,38,36,37,41,39,40,44,42,52,47,45,46,50,
%U 48,49,53,78,61,56,54,55,59,57,58,62,60,70,65,63,64,68,66
%N "Sloping ternary numbers": write numbers in ternary under each other (right-justified), read diagonals in upward direction, convert to decimal.
%C All terms are distinct, but certain terms (see A109682) are missing.
%C For the terms 3^k-1 (all 2's in ternary), the diagonal is not started at the leading 2, but at the leading 1 of the following term. - _Georg Fischer_, Mar 13 2020
%H Reinhard Zumkeller, <a href="/A109681/b109681.txt">Table of n, a(n) for n = 0..10000</a>
%H Georg Fischer, <a href="/A109681/a109681.pl.txt">Perl program</a>
%e number diagonal decimal
%e 0 0 0
%e 1 1 1
%e 2 12 5
%e 10 10 3
%e 11 11 4
%e 12 22 8
%e 20 20 6
%e 21 121 16
%e 22 102 11
%e 100 100 9
%e 101 101 10
%e 102 112 14
%e 110 110 12
%e 11. ... ...
%e 1.
%e .
%p t:= (n, i)-> (d-> `if`(i=0, d, t(m, i-1)))(irem(n, 3, 'm')):
%p b:= (n, i)-> `if`(3^i>n, 0, t(n,i) +3*b(n+1, i+1)):
%p a:= n-> b(n, 0):
%p seq(a(n), n=0..100); # _Alois P. Heinz_, Mar 13 2020
%o (Haskell)
%o a109681 n = a109681_list !! n
%o a109681_list = map (foldr (\d v -> 3 * v + d) 0) $ f a030341_tabf where
%o f vss = (g 0 vss) : f (tail vss)
%o g k (ws:wss) = if k < length ws then ws !! k : g (k + 1) wss else []
%o -- _Reinhard Zumkeller_, Nov 19 2013
%o (Perl) Cf. link.
%Y Cf. A109682 (complement), A109683 (ternary version), A109684.
%Y Cf. A102370 (base 2), A325644 (base 4), A325645 (base 5), A325692 (base 6), A325693 (base 7), A325805 (base 8), A325829 (base 9), A103205 (base 10).
%Y Cf. A030341.
%K nonn,nice,easy,base
%O 0,3
%A _Philippe Deléham_, Aug 08 2005
%E Conjectured g.f. and recurrence removed by _Georg Fischer_, Mar 13 2020
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