cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

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.

Crossrefs

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

Programs

  • 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 *)

Extensions

Name corrected by Charles R Greathouse IV, Sep 04 2015

A184872 n+floor(nr/s)+floor(nt/s), where r=log(2), s=log(3), t=log(5).

Original entry on oeis.org

2, 5, 8, 11, 15, 17, 21, 24, 27, 30, 33, 36, 40, 42, 45, 49, 51, 55, 57, 61, 64, 67, 70, 74, 76, 80, 83, 86, 89, 91, 95, 98, 101, 104, 108, 110, 114, 116, 120, 123, 126, 129, 132, 135, 138, 142, 144, 148, 150, 154, 157, 160, 163, 167, 169, 173, 175, 178, 182, 184, 188, 191, 194, 197, 201, 203, 207, 209, 213, 216, 219, 222, 225, 228, 231, 234, 237, 241, 243, 247, 250, 253, 256, 259, 262, 265, 268, 271, 275, 277, 281, 284, 287, 290, 293, 296, 300, 302, 306, 309, 311, 315, 317, 321, 324, 327, 330, 334, 336, 340, 343, 346, 349, 352, 355, 358, 361, 364, 368, 370
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Comments

See A184871.

Crossrefs

Cf. A184871, A184873, A184875 (primes in A184872).

Programs

  • 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 *)

A184874 Numbers m such that prime(m) is of the form k+floor(ks/r)+floor(kt/r), where r=log(2), s=log(3), t=log(5).

Original entry on oeis.org

6, 8, 9, 14, 16, 25, 28, 31, 32, 33, 36, 52, 57, 61, 65, 69, 71, 73, 78, 79, 82, 83, 95, 97, 111, 112, 113, 118, 121, 125, 126, 136, 140, 146, 147, 151, 154, 155, 156, 160, 167, 171, 176, 179, 180, 183, 185, 193, 194, 197, 209, 215, 220, 225, 233, 234, 240, 244, 249, 250, 255, 256, 260, 261, 262, 265, 268, 271, 287, 289, 293, 302, 312, 317, 324, 325, 329, 331, 335, 339, 357, 360, 361, 363, 365, 367, 369, 370, 374, 385, 386, 389, 392, 394, 396, 400, 404, 406, 408, 417
Offset: 1

Views

Author

Clark Kimberling, Jan 23 2011

Keywords

Comments

A184874, A184875, A184876 partition the primes.
A184874: 7,23,41,... of the form n+[ns/r]+[nt/r].
A184875: 3,11,19,31,... of the form n+[nr/s]+[nt/s].
A184876: 2,5,13,17,29,... of the form n+[nr/t]+[ns/t].
The Mathematica code can be easily modified to print
primes in the three classes.

Examples

			See A184871.

Crossrefs

Cf. A184871, A184872, A184873, A184875, A184876.

Programs

  • 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 *)
t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1;
t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2;
t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,600}];t3
t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4;
t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5;
t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,600}];t6
t7={};Do[If[PrimeQ[c[n]], AppendTo[t7,c[n]]],{n,1,600}];t7;
t8={};Do[If[PrimeQ[c[n]], AppendTo[t8,n]],{n,1,600}];t8;
t9={};Do[If[MemberQ[t7,Prime[n]],AppendTo[t9,n]],{n,1,600}];t9
(* Lists t3, t6, t9 match A184874, A184875, A184876. *)
PrimePi/@Select[Table[k+Floor[(k Log[3])/Log[2]]+Floor[(k Log[5])/Log[2]],{k,600}],PrimeQ] (* Harvey P. Dale, Apr 30 2025 *)
Showing 1-3 of 3 results.

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