A267703 Conjectured list of numbers whose trajectory under the '7x+1' map eventually reaches 1.

1, 2, 4, 5, 8, 9, 10, 16, 18, 20, 32, 36, 40, 41, 64, 72, 73, 80, 82, 128, 144, 146, 160, 164, 167, 256, 288, 292, 320, 328, 329, 334, 512, 576, 584, 585, 640, 656, 658, 668, 1024, 1152, 1168, 1170, 1280, 1312, 1316, 1336, 1337, 1965, 2048, 2304, 2336, 2340, 2560

Offset: 1

Author

Michel Lagneau, Jan 19 2016

Keywords

• nonn

Comments

This is conjectural in that there is no known proof that the missing numbers 3, 6, 7, ... are really missing. It may be that after a very large number of iterations they will cycle. - N. J. A. Sloane, Jan 23 2016

Note that the computer program does not actually calculate a complete list of "numbers k such that the Collatz-like map T: if x odd, x -> 7*x+1 and if x even, x -> x/2, when started at k, eventually reaches 1".

Examples

			5 is in the sequence because the trajectory of 5 is 5 -> 36 -> 18 -> 9 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1.
		

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..164

Crossrefs

Cf. A000079, A006577, A023001, A232711, A267969, A267970.

Programs

Maple

nn:=10000:
for n from 1 to 2340 do:
  m:=n:cyc:={n}:
    for i from 1 to nn do:
     if irem(m,2)=0
      then
       m:=m/2:
      else
      m:=7*m+1:
     fi:
    cyc:=cyc union {m}:
    od:
    n0:=nops(cyc):
    if n0N. J. A. Sloane, Jan 23 2016)

Extensions

Entry revised by N. J. A. Sloane, Jan 23 2016

a(19)-a(55) from Dmitry Kamenetsky, Jun 24 2024