|
%I #8 Nov 21 2013 12:47:49
%S 1,1,5,4,4,14,10,26,17,13,35,23,53,33,71,43,89,53,107,63,125,73,143,
%T 83,161,93,179,103,197,113,215,123,233,133,251,143,269,153,287,163,
%U 305,173,323,183,341,193,359,203,377,213,395,223,413,233,431,243,449,253
%N a(1)=1, a(n+1)=(a(n)+n)/2 if a(n)+n is even, a(n+1)=(3*(a(n)+n)+1)/2 otherwise.
%C Let a(1) be any integer >=0, is there always a positive integer N such that if n>=N a(n+2)-a(n)= 10 or 18 (depending on the parity of n)?
%F For k>=1 a(2k+12)=13+10k, a(2k+11)=17+18k
%t nxt[{a_,b_}]:=If[EvenQ[a+b],{a+1,(a+b)/2},{a+1,(3(b+a)+1)/2}]; Transpose[ NestList[nxt,{1,1},60]][[2]] (* _Harvey P. Dale_, Apr 01 2012 *)
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, May 29 2002
|
