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A337150 Nonnegative integers in the order in which they appear first in A006577.

%I A337150 #28 Oct 06 2021 07:56:16
%S A337150 0,1,7,2,5,8,16,3,19,6,14,9,17,4,12,20,15,10,23,111,18,106,26,13,21,
%T A337150 34,109,29,104,11,24,112,32,107,27,102,22,115,35,110,30,92,105,118,25,
%U A337150 87,38,100,113,69,33,95,46,108,121,28,41,90,103,116,36,85,54
%N A337150 Nonnegative integers in the order in which they appear first in A006577.
%C A337150 This is A006577 with duplicates removed.
%C A337150 This is a permutation of the nonnegative integers.
%H A337150 Alois P. Heinz, <a href="/A337150/b337150.txt">Table of n, a(n) for n = 1..1000</a>
%H A337150 Wikipedia, <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">Collatz Conjecture</a>
%H A337150 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%H A337150 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A337150 a(n) = A006577(A337149(n)).
%F A337150 a(n) = A006577(n) for 1 <= n <= 12.
%p A337150 collatz:= proc(n) option remember; `if`(n=1, 0,
%p A337150    1 + collatz(`if`(n::even, n/2, 3*n+1)))
%p A337150 end:
%p A337150 b:= proc() 0 end:
%p A337150 g:= proc(n) option remember; local t;
%p A337150      `if`(n=1, 0, g(n-1));
%p A337150       t:= collatz(n); b(t):= b(t)+1
%p A337150     end:
%p A337150 h:= proc(n) option remember; local k; for k
%p A337150       from 1+h(n-1) while g(k)>1 do od; k
%p A337150     end: h(0):=0:
%p A337150 a:= n-> collatz(h(n)):
%p A337150 seq(a(n), n=1..100);
%t A337150 collatz[n_] := collatz[n] = If[n==1, 0,
%t A337150    1 + collatz[If[EvenQ[n], n/2, 3n+1]]];
%t A337150 b[_] = 0;
%t A337150 g[n_] := g[n] = Module[{t}, If[n==1, 0, g[n-1]];
%t A337150    t = collatz[n]; b[t] = b[t]+1];
%t A337150 h[n_] := h[n] = Module[{k}, For[k = 1+h[n-1],
%t A337150    g[k]>1, k++]; k]; h[0] = 0;
%t A337150 a[n_] := a[n] = collatz[h[n]];
%t A337150 Array[a, 100] (* _Jean-François Alcover_, Jan 30 2021, after _Alois P. Heinz_ *)
%Y A337150 Cf. A006577, A337149.
%K A337150 nonn,look
%O A337150 1,3
%A A337150 _Alois P. Heinz_, Jan 27 2021