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%I #58 Apr 04 2024 12:52:42
%S 1,0,0,1,1,0,0,0,0,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0,0,0,1,0,0,0,0,0,0,
%T 0,0,1,0,1,1,0,1,0,1,0,0,0,0,0,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,
%U 0,1,0,0,0,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0,0,1,0,0,1,1,1,1,0,0,0,0,0
%N Square array read by antidiagonals upwards in which row n lists the parity of the 3x+1 sequence starting in n, with n >= 1 and k >= 0.
%H Paolo Xausa, <a href="/A347283/b347283.txt">Table of n, a(n) for n = 1..11325</a> (antidiagonals 1..150 of the array, flattened)
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F T(n,k) = A000035(A347270(n,k)), n >= 1, k >= 0.
%e The corner of the square array begins:
%e 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...
%e 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...
%e 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...
%e 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, ...
%e 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, ...
%e 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, ...
%e 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, ...
%e 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...
%e 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, ...
%e 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...
%e 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, ...
%e 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...
%e 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...
%e 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, ...
%e 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, ...
%e 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...
%e 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, ...
%e 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, ...
%e 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, ...
%e 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, ...
%e ...
%t A347283list[dmax_]:=With[{a=Mod[Array[NestList[If[OddQ[#],3#+1,#/2]&,dmax-#,#]&,dmax,0],2]},Array[Diagonal[a,#]&,dmax,1-dmax]];A347283list[20] (* Generates 20 antidiagonals *) (* _Paolo Xausa_, May 25 2023 *)
%Y Row 1 gives A079978.
%Y Column 1 gives A059841.
%Y Main diagonal (A371690) gives the parity of A347272.
%Y Rows n lists the parity of the following sequences: A153727 (n=1), A033478 (n=3), A033479 (n=9), A033480 (n=15), A033481 (n=21), A008884 (n=27), A008880 (n=33), A008878 (n=39), A008883 (n=51), A008877 (n=57), A008874 (n=63), A258056 (n=75), A258098 (n=79), A008876 (n=81), A008879 (n=87), A008875 (n=95), A008873 (n=97), A008882 (n=99), A245671 (n=1729).
%Y Columns k lists the parity of the following sequences: A000027 (k=0), A006370 (k=1), A075884 (k=2), A076536 (k=3).
%Y Cf. A347270 (gives all 3x+1 sequences).
%Y Cf. A000035 (parity), A014682, A220182, A339694.
%K nonn,tabl
%O 1
%A _Omar E. Pol_, Aug 26 2021
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