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

%I A267703 #33 Jun 26 2024 02:30:11
%S A267703 1,2,4,5,8,9,10,16,18,20,32,36,40,41,64,72,73,80,82,128,144,146,160,
%T A267703 164,167,256,288,292,320,328,329,334,512,576,584,585,640,656,658,668,
%U A267703 1024,1152,1168,1170,1280,1312,1316,1336,1337,1965,2048,2304,2336,2340,2560
%N A267703 Conjectured list of numbers whose trajectory under the '7x+1' map eventually reaches 1.
%C A267703 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
%C A267703 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".
%H A267703 Dmitry Kamenetsky, <a href="/A267703/b267703.txt">Table of n, a(n) for n = 1..164</a>
%e A267703 5 is in the sequence because the trajectory of 5 is 5 -> 36 -> 18 -> 9 -> 64 -> 32 -> 16 -> 8 -> 4 -> 2 -> 1.
%p A267703 nn:=10000:
%p A267703 for n from 1 to 2340 do:
%p A267703   m:=n:cyc:={n}:
%p A267703     for i from 1 to nn do:
%p A267703      if irem(m,2)=0
%p A267703       then
%p A267703        m:=m/2:
%p A267703       else
%p A267703       m:=7*m+1:
%p A267703      fi:
%p A267703     cyc:=cyc union {m}:
%p A267703     od:
%p A267703     n0:=nops(cyc):
%p A267703     if n0<nn
%p A267703     then
%p A267703     printf(`%d, `,n):
%p A267703     fi:
%p A267703    od :
%p A267703 (Warning: bad program - will not find all the terms. - _N. J. A. Sloane_, Jan 23 2016)
%Y A267703 Cf. A000079, A006577, A023001, A232711, A267969, A267970.
%K A267703 nonn
%O A267703 1,2
%A A267703 _Michel Lagneau_, Jan 19 2016
%E A267703 Entry revised by _N. J. A. Sloane_, Jan 23 2016
%E A267703 a(19)-a(55) from _Dmitry Kamenetsky_, Jun 24 2024