A007336 Signature sequence of sqrt 2 (arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x). (Formerly M0137)

1, 2, 1, 3, 2, 1, 4, 3, 2, 5, 1, 4, 3, 6, 2, 5, 1, 4, 7, 3, 6, 2, 5, 8, 1, 4, 7, 3, 6, 9, 2, 5, 8, 1, 4, 7, 10, 3, 6, 9, 2, 5, 8, 1, 11, 4, 7, 10, 3, 6, 9, 2, 12, 5, 8, 1, 11, 4, 7, 10, 3, 13, 6, 9, 2, 12, 5, 8, 1, 11, 4, 14, 7, 10, 3, 13, 6, 9, 2, 12, 5, 15, 8, 1, 11, 4, 14, 7, 10, 3, 13, 6, 16, 9, 2

Offset

1,2

References

C. Kimberling, "Fractal Sequences and Interspersions", Ars Combinatoria, vol. 45 p 157 1997.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..1000

C. Kimberling, Interspersions

Dale Gerdemann, Plot of Adjacent Terms, YouTube Video, 2015.

Formula

If delete first occurrence of 1, 2, 3, ... the sequence is unchanged.

Mathematica

Take[ Transpose[ Sort[ Flatten[ Table[{i + j*Sqrt[2], i}, {i, 17}, {j, 15}], 1], #1[[1]] < #2[[1]] &]][[2]], 96] (* Robert G. Wilson v, Jul 24 2004 *)

Crossrefs

Cf. A007337.

Sequence in context: A227355 A226080 A167287 * A227539 A133334 A003603

Adjacent sequences: A007333 A007334 A007335 * A007337 A007338 A007339

Keyword

nonn,easy,nice,eigen

Author

N. J. A. Sloane, Clark Kimberling

Extensions

More terms from Robert G. Wilson v, Jul 24 2004

Status

approved