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%I #23 Jul 15 2021 19:02:08
%S 1,2,4,8,10,12,13,16,17,20,21,22,23,24,25,26,28,29,30,32,33,34,35,36,
%T 37,38,39,40,42,43,44,45,46,48,49,50,51,52,53,56,57,58,59,60,61,64,65,
%U 66,67,68,69,70,72,74,75,76,77,78,79,80,81,84,85,86,87,88
%N Numbers k that require fewer than k steps to reach 1 under the 3x+1 map.
%C Numbers k such that A006577(k) < k.
%C Is 5 the only positive number neither in this sequence, nor in A228014 (cf. Caldwell, Honaker)?
%H Chris K. Caldwell and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/cpage/469.html">Curio for 5</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e The trajectory of 13 under repeated applications of the Collatz map starts 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, requiring 9 steps to reach 1. 9 < 13, so 13 is a term of the sequence.
%t nsteps[n_] := -1 + Length @ NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &]; Select[Range[100], nsteps[#] < # &] (* _Amiram Eldar_, Jul 14 2021 *)
%o (PARI) a006370(n) = if(n%2==0, n/2, 3*n+1)
%o is(n) = my(x=n, i=0); while(1, if(x==1, if(i < n, return(1), return(0))); x=a006370(x); i++)
%Y Cf. A006370, A006577, A082984, A228014.
%K nonn
%O 1,2
%A _Felix Fröhlich_, Jul 14 2021