A005184 Self-contained numbers: odd numbers k whose Collatz sequence contains a higher multiple of k.
31, 83, 293, 347, 671, 19151, 2025797
Offset: 1
Examples
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".
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).
- Index entries for sequences related to 3x+1 (or Collatz) problem
Crossrefs
Programs
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Maple
T:= proc(n) option remember; `if`(n=1, 1, [n, T(`if`(n::even, n/2, 3*n+1))][]) end: q:= n-> ormap(x-> x>n and irem(x, n)=0, [T(n)]): select(q, [2*i-1$i=1..10000])[]; # Alois P. Heinz, Aug 04 2025 -
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 *) -
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)
Extensions
More terms from Robert G. Wilson v
Better description from Jack Brennen, Feb 07 2003
Comments