A189786 -id:A189786 - cp's OEIS frontend

A189785 a(n) = n+floor(n*r/s)+floor(nt/s); r=Pi/2, s=arcsin(5/13), t=arcsin(12/13).

6, 14, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 102, 110, 118, 126, 134, 142, 150, 158, 166, 174, 182, 190, 198, 206, 214, 222, 230, 238, 246, 254, 262, 270, 278, 286, 294, 302, 310, 318, 326, 334, 342, 350, 358, 366, 374, 380, 388, 396, 404, 412, 420, 428, 436, 444, 452, 460, 468, 476, 484, 492, 500, 508, 516, 524, 532, 540, 548

Offset: 1

Clark Kimberling, Apr 27 2011

nonn

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(5/13), t=arcsin(12/13) gives
a=A005408, b=A189785, c=A189786.  Note that r=s+t.
a(n) first differs from A017137(n-1) at n=48 (a(48)=380 but A017137(47)=382). - Nathaniel Johnston, May 16 2011

Cf. A189786, A189787, A004773.

r=Pi/2; s=ArcSin[5/13]; t=ArcSin[12/13];
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}]  (*A189785*)
Table[c[n], {n, 1, 120}]  (*A189786*)
Table[b[n]/2, {n, 1, 120}]  (*A189787*)
Table[c[n]/2, {n, 1, 120}]  (*A004773*)

A189787 a(n) = A189785(n)/2.

Original entry on oeis.org

3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135, 139, 143, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230, 234, 238, 242, 246, 250, 254, 258, 262, 266, 270, 274, 278, 282

Offset: 1

Clark Kimberling, Apr 27 2011

nonn

See A189785.

Cf. A189785, A189786.

Mathematica
```
(See A189785.)
```

Name corrected by Nathaniel Johnston and R. J. Mathar, May 16 2011

Comment and formula corrected by Jaroslav Krizek, Jul 29 2016

cp's OEIS Frontend

A189785 a(n) = n+floor(n*r/s)+floor(nt/s); r=Pi/2, s=arcsin(5/13), t=arcsin(12/13).

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