A080816 -id:A080816 - cp's OEIS frontend

A067433 Triangle in which row n gives trajectory of n under the map k -> k/3 if k is divisible by 3, otherwise k -> next multiple of 3, stopping when reaching 1 (the initial term n is not included).

1, 3, 1, 1, 6, 2, 3, 1, 6, 2, 3, 1, 2, 3, 1, 9, 3, 1, 9, 3, 1, 3, 1, 12, 4, 6, 2, 3, 1, 12, 4, 6, 2, 3, 1, 4, 6, 2, 3, 1, 15, 5, 6, 2, 3, 1, 15, 5, 6, 2, 3, 1, 5, 6, 2, 3, 1, 18, 6, 2, 3, 1, 18, 6, 2, 3, 1, 6, 2, 3, 1, 21, 7, 9, 3, 1, 21, 7, 9, 3, 1, 7, 9, 3

Offset: 1

Cino Hilliard, Mar 29 2003

These numbers converge to various last 3-digit endings and only to 2 last 2-digit numbers: 2,1 or 3,1. m=3. p=1 below. If m=2, p=1 you get the x+1 conjecture. If m=2, p=3 you get the 3x+1 conjecture. See Link for numbers with a large number of digits. Other conjectures are possible by trial-and-error input of m and n. It is interesting to note that for many m and p=m+1 the program converges to 1. However, for m prime and p=m+1 the program always converges to m^2, m, 1. Also for m+1 prime the program converges to m^2, m, 1 most of the time. An exception is m=6. The sequence converges but to what I call an uninteresting ending.

			4 -> 6 -> 2 -> 3 -> 1, so row 4 is 6,2,3,1. Row 5 is the same.

Cino Hilliard, The x+1 conjecture [Dead link]

Cf. A080816.

nxt[n_]:=If[Divisible[n,3],n/3,3(Floor[n/3]+1)]; Join[{1},Flatten[ Table[ Rest[ NestWhileList[nxt,i,#!=1&]],{i,30}]]] (* Harvey P. Dale, Sep 16 2012 *)

multxp2(n,m,p) = { print1(1" "); for(j=1,n, x=j; c=0; while(x>1, r = x%m; if(r==0,x=x/m,x=x*p+m-r); print1(x" "); ); ) }

Corrected by Harvey P. Dale, Sep 16 2012

cp's OEIS Frontend

A067433 Triangle in which row n gives trajectory of n under the map k -> k/3 if k is divisible by 3, otherwise k -> next multiple of 3, stopping when reaching 1 (the initial term n is not included).

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