%I A124168
%S A124168 1,2,3,4,5,7,8,13,15,16,21,24,29,31,32,34,44,55,56,61,63,64,81,89,108,
%T A124168 120,125,127,128,144,149,208,233,236,248,253,255,256,274,377,401,464,
%U A124168 492,504,509,511,512,610,773,912,927,976,987,1004,1016,1021,1023,1024
%N A124168 Union of all n-Fibonacci sequences, that is, all sequences s(0) = s(1) 
               = ... = s(n-2) = 0, s(n-1) = 1 and for k >= n, s(k) = s(k-1) + ... 
               + s(k-n).
%C A124168 Note that an n-Fibonacci sequence contains the numbers 2^k numbers for 
               k<n. We also get 2^n-1, 2^(n+1)-3, 2^(n+2)-8, ... The sequence -1, 
               -3, -8, continues following A001792 (for n large)...
%C A124168 Noe and Post conjectured that the only positive terms that are common 
               to any two distinct n-step Fibonacci sequences are the powers of 
               2 that begin each sequence and 13 (in 2- and 3-step) and 504 (in 
               3- and 7-step). Perhaps we should also include 8 (in 2- and 4-step). 
               - T. D. Noe, Dec 05 2006
%H A124168 T. D. Noe, <a href="b124168.txt">Table of n, a(n) for n=1..1000</a>
%H A124168 Tony D. Noe and Jonathan Vos Post, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/VOL8/Noe/noe5.pdf">Primes in Fibonacci n-step and Lucas 
               n-step Sequences,</a> J. of Integer Sequences, Vol. 8 (2005), Article 
               05.4.4
%F A124168 Union(A000045, A000073, A000078, A001591, A001592, ...)
%t A124168 NFib25[nfb_] := Transpose[NestList[Join[Drop[ #, {1}], {Plus @@ #}] &, 
               Map[If[ # == nfb, 1, 0] &, Range[nfb]], 25]][[ -1]]; Union[Flatten[Map[NFib25, 
               Range[2, 20]]]][[Range[100]]]
%Y A124168 Cf. A000045, A000073, A000078, A001591, A001592, A124257.
%Y A124168 Sequence in context: A111795 A046098 A091997 this_sequence A054762 A039088 
               A111794
%Y A124168 Adjacent sequences: A124165 A124166 A124167 this_sequence A124169 A124170 
               A124171
%K A124168 nonn
%O A124168 1,2
%A A124168 Carlos Alves (cjsalves(AT)gmail.com), Dec 03 2006
%E A124168 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 15 2006