OFFSET
1,1
COMMENTS
The Collatz sequence of a number k is defined as a(1)=k, a(j+1) = a(j)/2 if a(j) is even, 3*a(j) + 1 if a(j) is odd.
No others less than 250000000. - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 07 2006
There are no more terms < 10^11. - Donovan Johnson, Nov 28 2013
There are no more terms < 10^15. - Alun Stokes, Mar 01 2021
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, E16.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alexander Rahn, Max Henkel, Sourangshu Ghosh, Eldar Sultanow, and Idriss Aberkane, An algorithm for linearizing Collatz convergence, hal-03286608 [math.DS], 2021.
Eldar Sultanow, Christian Koch, and Sean Cox, Collatz Sequences in the Light of Graph Theory, Universität Potsdam (Germany, 2020).
EXAMPLE
The Collatz sequence of 31 is 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310 (see A008884) ... 310 is a multiple of 31, so the number 31 is "self-contained".
MATHEMATICA
isSelfContained[n_] := Module[{d}, d = n; While[d != 1, If[EvenQ[d], d = d/2, d = 3 * d + 1]; If[IntegerQ[d/n], Return[True]]]; Return[False]]; For[n = 1, n <= 250000000, n += 2, If[isSelfContained[n], Print[n]]]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 07 2006 *)
scnQ[n_] := MemberQ[Divisible[#, n] & / @Rest[NestWhileList[If[EvenQ[#], #/2, 3# + 1] &, n, # > 1 &]], True]; Select[Range[1, 2100001, 2], scnQ] (* Harvey P. Dale, Oct 21 2011 *)
PROG
(PARI) m=5; d=2; while(1, n=(3*m+1)\2; until(n==1, n=if(n%2, 3*n+1, n\2); if(n%m==0, print(m, " ", n); break)); m+=d; d=6-d)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v
Better description from Jack Brennen, Feb 07 2003
STATUS
approved