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A189395 a(n) = n + [n*s/r] + [n*t/r]; r=1, s=1/sqrt(2), t=sqrt(3). 8
2, 6, 10, 12, 16, 20, 23, 26, 30, 34, 37, 40, 44, 47, 50, 54, 58, 61, 64, 68, 71, 75, 78, 81, 85, 89, 92, 95, 99, 102, 105, 109, 113, 116, 119, 123, 127, 129, 133, 137, 140, 143, 147, 151, 153, 157, 161, 164, 167, 171, 175, 178, 181, 185, 188, 191, 195, 199, 202, 205, 209, 212, 216, 219, 222, 226, 230, 233, 236, 240, 243, 246, 250, 254, 257, 260, 264, 268, 270, 274, 278, 281, 284 (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

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

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

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

Taking r=1, s=1/sqrt(2), t=sqrt(3) gives

a=A189395, b=A189396, c=A189397.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

r=1; s=2^(-1/2); t=3^(1/2);

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

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

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

Table[a[n], {n, 1, 120}]  (*A189395*)

Table[b[n], {n, 1, 120}]  (*A189396*)

Table[c[n], {n, 1, 120}]  (*A189397*)

CROSSREFS

Cf. A189396, A189397, A189361, A189383, A189386.

Sequence in context: A195064 A055743 A189680 * A190003 A263309 A190789

Adjacent sequences:  A189392 A189393 A189394 * A189396 A189397 A189398

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 21 2011

STATUS

approved

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Last modified October 17 22:05 EDT 2019. Contains 328134 sequences. (Running on oeis4.)