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A189399 n+[ns/r]+[nt/r]; r=1, s=sqrt(e), t=e. 4
4, 10, 15, 20, 26, 31, 37, 42, 47, 53, 58, 63, 69, 75, 79, 85, 91, 95, 101, 106, 112, 117, 122, 128, 133, 138, 144, 150, 154, 160, 166, 170, 176, 182, 187, 192, 198, 203, 209, 213, 219, 225, 229, 235, 241, 246, 251, 257, 262, 267, 273, 278, 284, 289, 294, 300, 304, 310, 316, 321, 326, 332, 337, 342, 348, 353, 359, 364, 369, 375, 380, 385, 391, 397, 401, 407, 412, 418, 423, 428, 434, 439 (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+[ns/r]+[nt/r],

b(n)=n+[nr/s]+[nt/s],

c(n)=n+[nr/t]+[ns/t], where []=floor.

Taking r=1, s=sqrt(e), t=e gives

a=A189399, b=A189400, c=A189401.

LINKS

Table of n, a(n) for n=1..82.

MATHEMATICA

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

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}]  (*A189399*)

Table[b[n], {n, 1, 120}]  (*A189400*)

Table[c[n], {n, 1, 120}]  (*A189401*)

CROSSREFS

Cf. A189400, A189401, A189402.

Sequence in context: A310460 A310461 A310462 * A310463 A310464 A310465

Adjacent sequences:  A189396 A189397 A189398 * A189400 A189401 A189402

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 21 2011

STATUS

approved

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Last modified August 19 08:37 EDT 2019. Contains 326115 sequences. (Running on oeis4.)