cp's OEIS Frontend

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).

%I A184874 #6 Apr 30 2025 13:19:26
%S A184874 6,8,9,14,16,25,28,31,32,33,36,52,57,61,65,69,71,73,78,79,82,83,95,97,
%T A184874 111,112,113,118,121,125,126,136,140,146,147,151,154,155,156,160,167,
%U A184874 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
%N 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).
%C A184874 A184874, A184875, A184876 partition the primes.
%C A184874 A184874: 7,23,41,... of the form n+[ns/r]+[nt/r].
%C A184874 A184875: 3,11,19,31,... of the form n+[nr/s]+[nt/s].
%C A184874 A184876: 2,5,13,17,29,... of the form n+[nr/t]+[ns/t].
%C A184874 The Mathematica code can be easily modified to print
%C A184874 primes in the three classes.
%e A184874 See A184871.
%t A184874 r=Log[2]; s=Log[3]; t=Log[5];
%t A184874 a[n_]:=n+Floor [n*s/r]+Floor[n*t/r];
%t A184874 b[n_]:=n+Floor [n*r/s]+Floor[n*t/s];
%t A184874 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t];
%t A184874 Table[a[n],{n,1,120}]  (* A184871 *)
%t A184874 Table[b[n],{n,1,120}]  (* A184872 *)
%t A184874 Table[c[n],{n,1,120}]  (* A184873 *)
%t A184874 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1;
%t A184874 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2;
%t A184874 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,600}];t3
%t A184874 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4;
%t A184874 t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5;
%t A184874 t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,600}];t6
%t A184874 t7={};Do[If[PrimeQ[c[n]], AppendTo[t7,c[n]]],{n,1,600}];t7;
%t A184874 t8={};Do[If[PrimeQ[c[n]], AppendTo[t8,n]],{n,1,600}];t8;
%t A184874 t9={};Do[If[MemberQ[t7,Prime[n]],AppendTo[t9,n]],{n,1,600}];t9
%t A184874 (* Lists t3, t6, t9 match A184874, A184875, A184876. *)
%t A184874 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 *)
%Y A184874 Cf. A184871, A184872, A184873, A184875, A184876.
%K A184874 nonn
%O A184874 1,1
%A A184874 _Clark Kimberling_, Jan 23 2011