

A167970


Signature sequence of phi^2 = 0.38196601125011..., where phi is the golden ratio 0.61803398874989... .


3



1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 3, 5, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 4, 1, 6, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 9, 1, 6, 3, 8, 5, 2
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OFFSET

1,4


REFERENCES

Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157168.


LINKS

Table of n, a(n) for n=1..105.


MATHEMATICA

terms = 105; m = Ceiling[Sqrt[terms]]; s0 = {}; While[s = (Table[i + j/GoldenRatio^2, {i, 1, m}, {j, 1, m}] // Flatten // SortBy[#, N] &)[[1 ;; terms]] /. GoldenRatio > \[Infinity]; s != s0, s0 = s; m = 2 m]; s (* JeanFrançois Alcover, Jan 08 2017 *)


CROSSREFS

Cf. A084531, A084532, A118276.
Sequence in context: A023132 A023124 A023120 * A126433 A237271 A176725
Adjacent sequences: A167967 A167968 A167969 * A167971 A167972 A167973


KEYWORD

nonn


AUTHOR

Casey Mongoven, Nov 15 2009


STATUS

approved



