A023118 Signature sequence of 1/sqrt(5) (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x).
1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 2, 3, 4, 5, 1, 6, 2, 7, 3, 4, 5, 1, 6, 2, 7, 3, 4, 5, 1, 6, 2, 7, 3, 8, 4, 5, 1, 6, 2, 7, 3, 8, 4, 5, 1, 6, 2, 7, 3, 8, 4, 9, 5, 1, 6, 2, 7, 3, 8, 4, 9, 5, 1, 6, 2, 7, 3, 8, 4, 9, 5, 1
Offset: 1
Keywords
References
- C. Kimberling, "Fractal Sequences and Interspersions", Ars Combinatoria, vol. 45 p 157 1997.
Links
- T. D. Noe, Table of n, a(n) for n=1..1000
- C. Kimberling, Interspersions
- Index entries for sequences related to signature sequences
Crossrefs
Cf. A020762.
Programs
-
Mathematica
signseq[n_] := Take[ Transpose[ Sort[ Flatten[ Table[{i + j*n, i}, {i, Max[15, 15n]}, {j, Max[15, 15/n]}], 1], #1[[1]] < #2[[1]] &]][[2]], 105]; signseq[1/Sqrt[5]] (* Robert G. Wilson v, Sep 20 2004 *)
Extensions
More terms from Robert G. Wilson v, Sep 20 2004