A249115 Floor(r*n), where r = (5 - sqrt(5))/2; the Beatty complement of A003231.

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

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*(5-Sqrt(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