

A249115


Floor(r*n), where r = (5  sqrt(5))/2; the Beatty complement of A003231.


3



1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 51, 52, 53, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 89, 91
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OFFSET

1,2


COMMENTS

Let r = (5  sqrt(5))/2 and s = (5 + sqrt(5))/2. Then 1/r + 1/s = 1, so that A249115 and A003231 are a pair of complementary Beatty sequences. Let tau = (1 + sqrt(5))/2, the golden ratio. Let R = {h*tau, h >= 1} and S = {k*(tau  1), k >= 1}. Then A249115(n) is the position of n*(tau  1) in the ordered union of R and S.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000
Scott V. Tezlaf, On ordinal dynamics and the multiplicity of transfinite cardinality, arXiv:1806.00331 [math.NT], 2018. See p. 9.


MATHEMATICA

Table[Floor[(5  Sqrt[5])/2*n], {n, 1, 200}]


PROG

(MAGMA) [Floor(n*(5Sqrt(5))/2): n in [1..100]]; // Vincenzo Librandi, Oct 25 2014


CROSSREFS

Cf. A003231, A001622.
Sequence in context: A280998 A043687 A087118 * A039032 A000062 A247964
Adjacent sequences: A249112 A249113 A249114 * A249116 A249117 A249118


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Oct 21 2014


STATUS

approved



