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A337149 Positive integers k such that the number of steps it takes to reach 1 in the '3x+1' problem is different for all j < k.

%I A337149 #26 Jan 31 2021 16:36:55
%S A337149 1,2,3,4,5,6,7,8,9,10,11,12,14,16,17,18,22,24,25,27,28,31,33,34,36,39,
%T A337149 41,43,47,48,49,54,57,62,65,71,72,73,78,82,86,91,94,97,98,103,105,107,
%U A337149 108,111,114,121,123,124,129,130,135,137,142,145,153,155,159
%N A337149 Positive integers k such that the number of steps it takes to reach 1 in the '3x+1' problem is different for all j < k.
%C A337149 Positive integers k such that A337144(k) = 1.
%C A337149 Or positive integers k such that A006577(k) != A006577(j) for all j = 1..k-1.
%C A337149 Different from A129304.
%H A337149 Alois P. Heinz, <a href="/A337149/b337149.txt">Table of n, a(n) for n = 1..1000</a>
%H A337149 Wikipedia, <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">Collatz Conjecture</a>
%H A337149 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A337149 A006577(a(n)) = A337150(n).
%p A337149 collatz:= proc(n) option remember; `if`(n=1, 0,
%p A337149    1 + collatz(`if`(n::even, n/2, 3*n+1)))
%p A337149 end:
%p A337149 b:= proc() 0 end:
%p A337149 g:= proc(n) option remember; local t;
%p A337149      `if`(n=1, 0, g(n-1));
%p A337149       t:= collatz(n); b(t):= b(t)+1
%p A337149     end:
%p A337149 a:= proc(n) option remember; local k; for k
%p A337149       from 1+a(n-1) while g(k)>1 do od; k
%p A337149     end: a(0):=0:
%p A337149 seq(a(n), n=1..100);
%t A337149 collatz[n_] := collatz[n] = If[n==1, 0,
%t A337149    1+collatz[If[EvenQ[n], n/2, 3n+1]]];
%t A337149 b[_] = 0;
%t A337149 g[n_] := g[n] = Module[{t}, If[n==1, 0, g[n-1]];
%t A337149    t = collatz[n]; b[t] = b[t]+1];
%t A337149 a[n_] := a[n] = Module[{k}, For[k = 1+a[n-1],
%t A337149    g[k] > 1, k++]; k]; a[0] = 0;
%t A337149 Array[a, 100] (* _Jean-François Alcover_, Jan 30 2021, after _Alois P. Heinz_ *)
%Y A337149 Cf. A006577, A129304, A337144, A337150.
%K A337149 nonn,look
%O A337149 1,2
%A A337149 _Alois P. Heinz_, Jan 27 2021