

A189756


n+[ns/r]+[nt/r]; r=1, s=sin(1), t=cos(1).


3



1, 4, 6, 9, 11, 14, 15, 18, 20, 23, 25, 28, 30, 32, 35, 37, 40, 42, 44, 46, 49, 51, 54, 56, 59, 61, 63, 66, 68, 71, 73, 75, 77, 80, 82, 85, 87, 89, 92, 94, 97, 99, 102, 104, 106, 108, 111, 113, 116, 119, 120, 123, 125, 128, 130, 133, 134, 137, 139, 142, 144, 147, 150, 151, 154, 156, 159, 161, 164, 165, 168, 170, 173, 175, 178, 180, 182
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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=1, s=sin(1), t=cos(1) gives


LINKS



FORMULA

a(n)=n+[n*sin(1)]+[n*cos(1)].


MATHEMATICA

r=1; s=Sin[1]; t=Cos[1];
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}] (*A189756*)
Table[b[n], {n, 1, 120}] (*A189757*)
Table[c[n], {n, 1, 120}] (*A189758*)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



