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

1,2

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".

Links

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

Example

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

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 n0<nn
    then
    printf(`%d, `, n):
    fi:
   od :
(Warning: bad program - will not find all the terms. - N. J. A. Sloane, Jan 23 2016)

Crossrefs

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

Sequence in context: A010402 A010443 A035269 * A277075 A038558 A286031

Adjacent sequences: A267700 A267701 A267702 * A267704 A267705 A267706

Keyword

nonn

Author

Michel Lagneau, Jan 19 2016

Extensions

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

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

Status

approved