A354170 - OEIS

%I #17 Jun 02 2022 22:02:05

%S 57,59,115,119,229,237,461,465,473,477,507,513,917,931,943,945,947,

%T 949,971,987,1015,1025,1027,1031,1129,1131,1845,1857,1861,1867,1881,

%U 1887,1891,1893,1905,1909,1943,1945,1953,1975,2029,2051,2053,2055,2059,2063,2073

%N Odd numbers whose Collatz trajectory includes 11 odd numbers.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">Collatz Conjecture</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F { A005408 } intersect { A072466 }. - _Alois P. Heinz_, May 18 2022

%e 119 is a term since its Collatz trajectory is 119, 358, 179, 538, 269, 808, 404, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 29, 10, 5, 16, 8, 4, 2, 1, which has 11 odd numbers.

%p b:= proc(n) option remember; irem(n, 2, 'r')+

%p       `if`(n=1, 0, b(`if`(n::odd, 3*n+1, r)))

%p     end:

%p q:= n-> is(n::odd and b(n)=11):

%p select(q, [$1..5000])[];  # _Alois P. Heinz_, May 18 2022

%t q[n_] := Count[NestWhileList[If[OddQ[#], 3 # + 1, #/2] &, n, # > 1 &], _?OddQ] == 11; Select[2*Range[1000] - 1, q] (* _Amiram Eldar_, May 18 2022 *)

%Y Cf. A005408, A072466, A072197.

%K nonn

%O 1,1

%A _Krishna Kumar Arumugam_, May 18 2022