A189521 n+[ns/r]+[nt/r]; r=1, s=1/(e-1), t=1/(e+1).

1, 3, 4, 7, 8, 10, 12, 14, 16, 17, 19, 21, 23, 25, 27, 29, 30, 32, 35, 36, 38, 39, 42, 43, 45, 47, 49, 51, 52, 55, 57, 58, 60, 62, 64, 65, 67, 70, 71, 73, 75, 77, 79, 80, 83, 84, 86, 87, 90, 92, 93, 95, 97, 99, 101, 103, 105, 106, 108, 110, 112, 114, 115, 118, 119, 121, 123, 125, 127, 128, 131, 132, 134, 136, 138, 140, 141, 143, 145, 147, 149, 151, 153, 154, 156

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=1/(e-1), t=1/(e+1) gives

a=A189521, b=A189522, c=A189523.

Links

Table of n, a(n) for n=1..85.

Mathematica

r=1; s=1/(E-1); t=1/(E+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}]  (*A189521*)
Table[b[n], {n, 1, 120}]  (*A189522*)
Table[c[n], {n, 1, 120}]  (*A189523*)

Crossrefs

Cf. A189522, A189523.

Sequence in context: A024515 A187835 A184820 * A285346 A244736 A138971

Adjacent sequences: A189518 A189519 A189520 * A189522 A189523 A189524

Keyword

nonn

Author

Clark Kimberling, Apr 23 2011

Status

approved