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A380244 The Collatz (or 3x+1) trajectory starting at a(n) contains exactly n odd integers and a(n) is the n-th number with this property.

%I A380244 #24 Jan 18 2025 19:49:37
%S A380244 1,10,12,68,45,30,72,101,134,179,237,314,422,551,723,509,1282,887,
%T A380244 1170,1535,2021,1509,1899,2412,1780,2217,3170,3867,2819,3728,2511,
%U A380244 3155,3972,2802,3578,2623,3444,4302,3087,3968,2690,1806,2336,1593,2084,2757,1884,2477
%N A380244 The Collatz (or 3x+1) trajectory starting at a(n) contains exactly n odd integers and a(n) is the n-th number with this property.
%H A380244 Alois P. Heinz, <a href="/A380244/b380244.txt">Table of n, a(n) for n = 1..235</a>
%H A380244 Wikipedia, <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">Collatz Conjecture</a>
%H A380244 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A380244 A078719(a(n)) = n.
%e A380244 a(2) = 10 is the second integer (after 5) having exactly two odd integers in the Collatz trajectory: 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1.
%p A380244 b:= proc(n) option remember; irem(n, 2, 'r')+
%p A380244       `if`(n=1, 0, b(`if`(n::odd, 3*n+1, r)))
%p A380244     end:
%p A380244 A:= proc() local h, p, q; p, q:= proc() [] end, 0;
%p A380244       proc(n, k)
%p A380244         if k=1 then return 2^(n-1) fi;
%p A380244         while nops(p(k))<n do q:= q+1;
%p A380244           h:= b(q);
%p A380244           p(h):= [p(h)[], q]
%p A380244         od; p(k)[n]
%p A380244       end
%p A380244     end():
%p A380244 a:= n-> A(n$2):
%p A380244 seq(a(n), n=1..48);
%Y A380244 Main diagonal of A354236.
%Y A380244 Cf. A006577, A006667, A078719, A337144.
%K A380244 nonn
%O A380244 1,2
%A A380244 _Alois P. Heinz_, Jan 17 2025