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%I #29 Apr 04 2024 12:52:38
%S 1,1,5,4,2,8,26,4,52,1,16,2,1,16,8,2,4,8,4,1,4,1,4,4,4,1,155,1,4,2,
%T 395,2,1,2,1,2,1,4,4,4,668,1,4,1,4,2,425,1,1,4,2,4,2,850,425,1,1,2,2,
%U 4,2,4858,2429,1,4,2,1,2,1,4,2308,4,3644,1,1,2,1,1,4,4,4
%N Main diagonal of the square array A347270.
%C A347270 is related to the 3x + 1 (or Collatz) problem.
%C Conjectures from _Alois P. Heinz_, Aug 31 2021: (Start)
%C a(n) in {1, 2, 4, 5, 8, 10, 16, 26, 52, 53, 106, 155, 395, 425, 488, 668, 850, 866, 1732, 2308, 2429, 3644, 4858} for n >= 0.
%C a(n) in {1, 2, 4} for n >= 110. (End)
%H Alois P. Heinz, <a href="/A347272/b347272.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%p b:= proc(n, k) option remember; `if`(k=0, n, (j->
%p `if`(j::even, j/2, 3*j+1))(b(n, k-1)))
%p end:
%p a:= n-> b(n+1, n):
%p seq(a(n), n=0..80); # _Alois P. Heinz_, Aug 25 2021
%t b[n_, k_] := b[n, k] = If[k == 0, n, Function[j,
%t If[EvenQ[j], j/2, 3*j + 1]][b[n, k - 1]]];
%t a[n_] := b[n + 1, n];
%t Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, Apr 07 2022, after _Alois P. Heinz_ *)
%Y Cf. A006370, A033478, A033479, A075884, A076536, A153727, A347270, A371690 (parity).
%K nonn
%O 0,3
%A _Omar E. Pol_, Aug 25 2021
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