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).

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

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

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 *)