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A030341 Triangle T(n,k): write n in base 3, reverse order of digits.

%I A030341 #34 Feb 16 2025 08:32:35
%S A030341 0,1,2,0,1,1,1,2,1,0,2,1,2,2,2,0,0,1,1,0,1,2,0,1,0,1,1,1,1,1,2,1,1,0,
%T A030341 2,1,1,2,1,2,2,1,0,0,2,1,0,2,2,0,2,0,1,2,1,1,2,2,1,2,0,2,2,1,2,2,2,2,
%U A030341 2,0,0,0,1,1,0,0,1,2,0,0,1,0,1,0,1,1,1,0,1,2,1,0,1
%N A030341 Triangle T(n,k): write n in base 3, reverse order of digits.
%H A030341 Reinhard Zumkeller, <a href="/A030341/b030341.txt">Rows n = 0..1000 of triangle, flattened</a>
%H A030341 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ternary.html">Ternary.</a>
%H A030341 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ternary_numeral_system">Ternary numeral system</a>
%e A030341 Triangle begins :
%e A030341 0
%e A030341 1
%e A030341 2
%e A030341 0, 1
%e A030341 1, 1
%e A030341 2, 1
%e A030341 0, 2
%e A030341 1, 2
%e A030341 2, 2
%e A030341 0, 0, 1
%e A030341 1, 0, 1
%e A030341 2, 0, 1
%e A030341 0, 1, 1
%e A030341 1, 1, 1
%e A030341 2, 1, 1 ...
%p A030341 A030341_row := n -> op(convert(n, base, 3)):
%p A030341 seq(A030341_row(n), n=0..32); # _Peter Luschny_, Nov 28 2017
%t A030341 Flatten[Table[Reverse[IntegerDigits[n,3]],{n,0,40}]] (* _Harvey P. Dale_, Oct 20 2014 *)
%o A030341 (Haskell)
%o A030341 a030341 n k = a030341_tabf !! n !! k
%o A030341 a030341_row n = a030341_tabf !! n
%o A030341 a030341_tabf = iterate succ [0] where
%o A030341    succ []     = [1]
%o A030341    succ (2:ts) = 0 : succ ts
%o A030341    succ (t:ts) = (t + 1) : ts
%o A030341 -- _Reinhard Zumkeller_, Feb 21 2013
%o A030341 (PARI) A030341(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.")*/n\3^k%3 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030567 and others. - _M. F. Hasler_, Jul 21 2013
%Y A030341 Cf. A081604 (row lengths), A053735 (row sums), A007089, A003137.
%Y A030341 Cf. A030308, A030386, A031235, A030567, A031007, A031045, A031087, A031298 for the base-2 to base-10 analogs.
%K A030341 nonn,base,tabf,less
%O A030341 0,3
%A A030341 _Clark Kimberling_
%E A030341 Initial 0 and better name by _Philippe Deléham_, Oct 20 2011