

A189367


n+[ns/r]+[nt/r]; r=2, s=sqrt(2), t=sqrt(3).


3



1, 4, 7, 9, 12, 15, 17, 19, 22, 25, 27, 30, 33, 35, 37, 40, 43, 45, 48, 51, 53, 56, 58, 60, 63, 66, 69, 71, 74, 76, 78, 81, 84, 87, 89, 92, 95, 96, 99, 102, 104, 107, 110, 113, 114, 117, 120, 122, 125, 128, 131, 133, 135, 138, 140, 143, 146, 149, 151, 153, 156, 158, 161, 164, 166, 169, 172, 174, 176, 179, 182, 184, 187, 190, 192, 194, 197, 200, 202, 205, 208, 210, 212, 215
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OFFSET

1,2


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=2, s=sqrt(2), t=sqrt(3) gives
a=A189367, b=A189368, c=A189369.


LINKS

Table of n, a(n) for n=1..84.


MATHEMATICA

r = 2; 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}] (*A189367*)
Table[b[n], {n, 1, 120}] (*A189368*)
Table[c[n], {n, 1, 120}] (*A189369*)


CROSSREFS

Cf. A189368, A189369.
Sequence in context: A086824 A266936 A080574 * A007066 A260395 A047537
Adjacent sequences: A189364 A189365 A189366 * A189368 A189369 A189370


KEYWORD

nonn


AUTHOR

Clark Kimberling, Apr 20 2011


STATUS

approved



