

A124168


Union of all nFibonacci sequences, that is, all sequences s(0) = s(1) = ... = s(n2) = 0, s(n1) = 1 and for k >= n, s(k) = s(k1) + ... + s(kn).


5



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, 120, 125, 127, 128, 144, 149, 208, 233, 236, 248, 253, 255, 256, 274, 377, 401, 464, 492, 504, 509, 511, 512, 610, 773, 912, 927, 976, 987, 1004, 1016, 1021, 1023, 1024
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OFFSET

1,2


COMMENTS

Note that an nFibonacci sequence contains the numbers 2^k numbers for k<n. We also get 2^n1, 2^(n+1)3, 2^(n+2)8, ... The sequence 1, 3, 8, continues following A001792 (for n large)...
Noe and Post conjectured that the only positive terms that are common to any two distinct nstep Fibonacci sequences are the powers of 2 that begin each sequence and 13 (in 2 and 3step) and 504 (in 3 and 7step). Perhaps we should also include 8 (in 2 and 4step).  T. D. Noe, Dec 05 2006


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci nstep and Lucas nstep Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4


FORMULA

Union(A000045, A000073, A000078, A001591, A001592, ...)


MATHEMATICA

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]]]
NFib[nfb_, lim_] := Module[{f = 2^Range[0, nfb  1]}, While[f[[1]] <= lim, AppendTo[f, Total[Take[f, nfb]]]]; Most[f]]; lim = 12; Union[Flatten[Table[NFib[i, 2^lim], {i, 2, lim + 1}]]] (* T. D. Noe, Oct 25 2013 *)


CROSSREFS

Cf. A000045, A000073, A000078, A001591, A001592, A124257.
Cf. A227880 (primes here).
Sequence in context: A247350 A057484 A091997 * A309708 A285929 A309880
Adjacent sequences: A124165 A124166 A124167 * A124169 A124170 A124171


KEYWORD

nonn


AUTHOR

Carlos Alves, Dec 03 2006


EXTENSIONS

Edited by N. J. A. Sloane, Dec 15 2006


STATUS

approved



