

A127208


Union of all nstep Lucas sequences, that is, all sequences s(1n) = s(2n) = ... = s(1) = 1, s(0) = n and for k > 0, s(k) = s(k1) + ... + s(kn).


3



1, 3, 4, 7, 11, 15, 18, 21, 26, 29, 31, 39, 47, 51, 57, 63, 71, 76, 99, 113, 120, 123, 127, 131, 191, 199, 223, 239, 241, 247, 255, 322, 367, 439, 443, 475, 493, 502, 511, 521, 708, 815, 843, 863, 943, 983, 1003, 1013, 1023, 1364, 1365, 1499, 1695, 1871, 1959
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OFFSET

1,2


COMMENTS

Noe and Post conjectured that the only positive terms that are common to any two distinct nstep Lucas sequences are the Mersenne numbers (A001348) that begin each sequence and 7 and 11 (in 2 and 3step) and 5071 (in 3 and 4step). The intersection of this sequence with the union of all the nstep Fibonacci sequences (A124168) appears to consist of 4, 21, 29, the Mersenne numbers 2^n1 for all n and the infinite set of Eulerian numbers in A127232.


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(A000032, A001644, A073817, A074048, A074584, A104621, A105754, A105755,...)


MATHEMATICA

LucasSequence[n_, kMax_] := Module[{a, s, lst={}}, a=Join[Table[ 1, {n1}], {n}]; While[s=Plus@@a; a=RotateLeft[a]; a[[n]]=s; s<=kMax, AppendTo[lst, s]]; lst]; nn=10; t={}; Do[t=Union[t, LucasSequence[n, 2^(nn+1)]], {n, 2, nn}]; t


CROSSREFS

Cf. A227885.
Sequence in context: A023563 A050120 A039010 * A027022 A120365 A166375
Adjacent sequences: A127205 A127206 A127207 * A127209 A127210 A127211


KEYWORD

nonn


AUTHOR

T. D. Noe, Jan 09 2007


STATUS

approved



