A184871 n+floor(ns/r)+floor(nt/r), where r=log(2), s=log(3), t=log(5).

4, 9, 13, 19, 23, 28, 34, 38, 43, 48, 53, 58, 63, 68, 72, 78, 82, 87, 93, 97, 102, 107, 112, 117, 122, 127, 131, 137, 141, 146, 151, 156, 161, 165, 171, 176, 180, 186, 190, 195, 200, 205, 210, 215, 220, 224, 230, 235, 239, 245, 249, 254, 260, 264, 269, 274, 279, 283, 288, 294, 298, 303, 308, 313, 318, 323, 328, 332, 338, 342, 347, 353, 357, 362, 367, 372, 377, 382, 387, 391, 397, 401, 406, 412, 416, 421, 426, 431, 436, 440, 446, 450, 455, 460, 465, 470, 475, 480, 484, 490, 495, 499, 505, 509, 514, 520, 524, 529, 534, 539, 543, 549, 554, 558, 564, 568, 573, 578, 583, 588

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 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=log(2), s=log(3), t=log(5) yields

a=A184871, b=A184872, c=A184873.

Links

Table of n, a(n) for n=1..120.

Mathematica

r=Log[2]; s=Log[3]; t=Log[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}]  (* A184871 *)
Table[b[n], {n, 1, 120}]  (* A184872 *)
Table[c[n], {n, 1, 120}]  (* A184873 *)

Crossrefs

Cf. A184812, A184872, A184873, A184874 (primes in A184872).

Sequence in context: A312972 A312973 A312974 * A184912 A312975 A312976

Adjacent sequences: A184868 A184869 A184870 * A184872 A184873 A184874

Keyword

nonn

Author

Clark Kimberling, Jan 23 2011

Extensions

Name corrected by Charles R Greathouse IV, Sep 04 2015

Status

approved