

A081246


Triangle in which (2^n+1)st row gives trajectory of x=2^n+1 under the map x > x/2 if x is even, x > x+1 if x is odd, stopping when reaching 1.


0



3, 4, 2, 1, 5, 6, 3, 4, 2, 1, 9, 10, 5, 6, 3, 4, 2, 1, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 129, 130, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 257, 258, 129, 130, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1, 513, 514, 257, 258, 129, 130, 65, 66, 33, 34, 17, 18, 9, 10, 5, 6, 3, 4, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This is the 2^n+1 conjecture and is easily proved to converge to 1. The number of steps required to reach 1 is always 2n+2. Since (2^(n)+1+1)/2 = 2^(n1)+1 (2^(n1)+1+1)/2 = 2^(n2)+1 .... (2^(nn+1)+1+1)/2 = 2^(nn)+1 = 2 2/2 = 1 thus 1 is guaranteed.


LINKS



EXAMPLE

n = 5 > 33,34,17,18,9,10,5,6,3,4,2,1


MAPLE

pxpr(n) = { for(x=1, n, x1=2^x+1; print1(x1" "); while(x1>1, if(x1%2==0, x1/=2, x1 = x1+1); print1(x1" "); ) ) }


MATHEMATICA

Table[NestWhileList[If[EvenQ[#], #/2, #+1]&, 2^n+1, #!=1&], {n, 10}]//Flatten (* Harvey P. Dale, Jan 05 2019 *)


CROSSREFS



KEYWORD

easy,nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



