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A267703
Conjectured list of numbers whose trajectory under the '7x+1' map eventually reaches 1.
2
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
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
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