%I A081246
%S A081246 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,
%T A081246 18,9,10,3,4,2,1,65,66,33,34,17,18,9,10,5,6,3,4,2,1,129,130,65,66,33,34,
%U A081246 17,18,9,10,5,4,2,1,257,258,129,130,65,66,33,34,17,18,9,10,5,6,3,4,2,1
%N 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.
%C A081246 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^(n-1)+1 (2^(n-1)+1+1)/2 = 2^(n-2)+1 .... (2^(n-n+1)+1+1)/2 
               = 2^(n-n)+1 = 2 2/2 = 1 thus 1 is guaranteed.
%e A081246 n = 5 -> 33,34,17,18,9,10,5,6,3,4,2,1
%p A081246 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" "); ) ) }
%Y A081246 Sequence in context: A145425 A070352 A136374 this_sequence A096411 A143486 
               A159273
%Y A081246 Adjacent sequences: A081243 A081244 A081245 this_sequence A081247 A081248 
               A081249
%K A081246 easy,nonn,tabf
%O A081246 1,1
%A A081246 Cino Hilliard (hillcino368(AT)gmail.com), Apr 19 2003