A354170 Odd numbers whose Collatz trajectory includes 11 odd numbers.

57, 59, 115, 119, 229, 237, 461, 465, 473, 477, 507, 513, 917, 931, 943, 945, 947, 949, 971, 987, 1015, 1025, 1027, 1031, 1129, 1131, 1845, 1857, 1861, 1867, 1881, 1887, 1891, 1893, 1905, 1909, 1943, 1945, 1953, 1975, 2029, 2051, 2053, 2055, 2059, 2063, 2073

Offset: 1

Author

Krishna Kumar Arumugam, May 18 2022

Keywords

• nonn

Examples

			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.
		

Links

• Wikipedia, Collatz Conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A005408, A072466, A072197.

Programs

Maple

b:= proc(n) option remember; irem(n, 2, 'r')+
      `if`(n=1, 0, b(`if`(n::odd, 3*n+1, r)))
    end:
q:= n-> is(n::odd and b(n)=11):
select(q, [$1..5000])[];  # Alois P. Heinz, May 18 2022

Mathematica

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

Formula

{ A005408 } intersect { A072466 }. - Alois P. Heinz, May 18 2022