A189676 a(n) = n + [nr/s] + [nt/s]; r=Pi/2, s=arcsin(3/5), t=arcsin(4/5).

4, 8, 14, 18, 24, 28, 34, 38, 42, 48, 52, 58, 62, 68, 72, 78, 82, 86, 92, 96, 102, 106, 112, 116, 122, 126, 130, 136, 140, 146, 150, 156, 160, 164, 170, 174, 180, 184, 190, 194, 200, 204, 208, 214, 218, 224, 228, 234, 238, 244, 248, 252, 258, 262, 268, 272, 278, 282, 288, 292, 296, 302, 306, 312, 316, 322, 326, 330, 336, 340, 346

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=Pi/2, s=arcsin(3/5), t=arcsin(4/5) gives a=A005408, b=A189676, c=A189680.

Links

Table of n, a(n) for n=1..71.

Mathematica

r=Pi/2; s=ArcSin[3/5]; t=ArcSin[4/5];
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}]  (*A005408*)
Table[b[n], {n, 1, 120}]  (*A189676*)
Table[c[n], {n, 1, 120}]  (*A189680*)

Crossrefs

Cf. A005408 (the odd numbers), A189681=(A189676)/2, A189672=(A189680)/2, A189680.

Sequence in context: A312553 A312554 A312555 * A312556 A312557 A312558

Adjacent sequences: A189673 A189674 A189675 * A189677 A189678 A189679

Keyword

nonn

Author

Clark Kimberling, Apr 25 2011

Status

approved