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A190344 a(n) = n + [n*s/r] + [n*t/r]; r=1, s=sqrt(5/2), t=sqrt(2/5). 3
2, 6, 8, 12, 15, 18, 22, 25, 28, 31, 34, 37, 41, 44, 47, 51, 53, 57, 61, 63, 67, 69, 73, 76, 79, 83, 86, 89, 92, 95, 99, 102, 105, 108, 112, 114, 118, 122, 124, 128, 130, 134, 137, 140, 144, 147, 150, 153, 156, 160, 163, 166, 169, 173, 175, 179, 183, 185, 189, 191, 195, 199, 201, 205, 208, 211, 214, 218, 221, 224, 227, 230, 234, 237 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is one of three sequences that partition the positive integers.  In general, suppose that r, s, t are positive real numbers for which the sets {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are pairwise disjoint.  Let a(n) be the rank of n/r when all the numbers in the three sets are jointly ranked.  Define b(n) and c(n) as the ranks of n/s and n/t.  It is easy to prove that

f(n) = n + [n*s/r] + [n*t/r],

g(n) = n + [n*r/s] + [n*t/s],

h(n) = n + [n*r/t] + [n*s/t], where []=floor.

Taking r=1, s=sqrt(5/2), t=sqrt(2/5) gives f=A190344, g=A190345, h=A190346.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

A190344:  f(n) = n + [n*sqrt(5/2)] + [n*sqrt(2/5)].

A190345:  g(n) = n + [n*sqrt(2/5)] + [2*n/5].

A190346:  h(n) = 3*n + [n*sqrt(5/2)] + [n/2].

MATHEMATICA

r=1; s=(5/2)^(1/2); t=1/s;

f[n_] := n + Floor[n*s/r] + Floor[n*t/r];

g[n_] := n + Floor[n*r/s] + Floor[n*t/s];

h[n_] := n + Floor[n*r/t] + Floor[n*s/t];

Table[f[n], {n, 1, 120}]  (* A190344 *)

Table[g[n], {n, 1, 120}]  (* A190345 *)

Table[h[n], {n, 1, 120}]  (* A190346 *)

PROG

(PARI) for(n=1, 100, print1(n + floor(n*sqrt(5/2)) + floor(n*sqrt(2/5)), ", ")) \\ G. C. Greubel, Apr 05 2018

(MAGMA) [n + Floor(n*Sqrt(5/2)) + Floor(n*Sqrt(2/5)): n in [1..100]]; // G. C. Greubel, Apr 05 2018

CROSSREFS

Cf. A190345, A190346.

Sequence in context: A138626 A178406 A189515 * A287000 A282358 A064796

Adjacent sequences:  A190341 A190342 A190343 * A190345 A190346 A190347

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 09 2011

STATUS

approved

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Last modified August 22 15:37 EDT 2019. Contains 326178 sequences. (Running on oeis4.)