login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072939 Define a sequence c depending on n by: c(1)=1 and c(2)=n; c(k+2) = (c(k+1) + c(k))/2 if c(k+1) and c(k) have the same parity; otherwise c(k+2)=abs(c(k+1)-2*c(k)); sequence gives values of n such that lim k -> infinity c(k) = infinity. 7

%I

%S 3,7,9,11,15,19,23,25,27,31,33,35,39,41,43,47,51,55,57,59,63,67,71,73,

%T 75,79,83,87,89,91,95,97,99,103,105,107,111,115,119,121,123,127,129,

%U 131,135,137,139,143,147,151,153,155,159,161,163,167,169,171,175,179

%N Define a sequence c depending on n by: c(1)=1 and c(2)=n; c(k+2) = (c(k+1) + c(k))/2 if c(k+1) and c(k) have the same parity; otherwise c(k+2)=abs(c(k+1)-2*c(k)); sequence gives values of n such that lim k -> infinity c(k) = infinity.

%C If c(2) is even then c(k) = 1 for k >= 2*c(2), hence there is no even value in the sequence. If n is in the sequence, there is an integer k(n) and an integer m(n) such that for any k >= k(n) c(2k)-c(2k-1) = 2*m(n) and c(2k+1)-c(2k)=-m(n). Sometimes m(n) = (n-1)/2 but not always. If B(n) = a(n+1)-a(n) then B(n) = 2 or 4, but B(n) does not seem to follow any pattern.

%C Conjecture: a(n) = A036554(n)+1. - _Vladeta Jovovic_, Apr 01 2003

%C a(n) = A036554(n)+1 = A079523(n)+2. - _Ralf Stephan_, Jun 09 2003

%C Conjecture: this sequence gives the positions of 0's in the limiting 0-word of the morphism 0->11, 1->10, A285384. - _Clark Kimberling_, Apr 26 2017

%C Conjecture: This also gives the positions of the 1's in A328979. - _N. J. A. Sloane_, Nov 05 2019

%F Conjecture : lim n -> infinity a(n)/n = 3.

%e if c(2)=41 -> c(3)= 21 ->c(4)= 31 ->c(5)= 26 ->c(6)= 36 ->c(7)= 31 ->c(8)= 41 ->c(9)= 36 then c(2k)-c(2k-1)= 10 c(2k+1)-c(2k) = - 5 for k >=2 implies that c(k) -> infinity hence 41 is in the sequence.

%Y Cf. A036554, A079523, A285384, A328979.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Aug 12 2002

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)