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A184815 Numbers m such that prime(m) is of the form k+floor(ks/r)+floor(kt/r), where r=sqrt(2), s=sqrt(3), t=sqrt(5).

%I A184815 #11 Jan 30 2018 09:48:17
%S A184815 2,4,10,12,13,16,22,29,30,36,42,44,45,49,52,57,59,60,64,70,71,76,82,
%T A184815 84,90,91,92,97,101,103,108,111,114,115,119,123,125,138,140,142,149,
%U A184815 150,165,171,178,180,182,185,189,191,192,193,195,198,205,211,215,217,220,222,224,233,235,236,247,248,249,252,254,255,264,265,269,273,286,295,301,302,306,307,309,316,318,325,326,327,328,329,332,336
%N A184815 Numbers m such that prime(m) is of the form k+floor(ks/r)+floor(kt/r), where r=sqrt(2), s=sqrt(3), t=sqrt(5).
%C A184815 A184815, A184816, and A184817 partition the primes:
%C A184815 A184815: 3,7,29,37,... of the form n+[ns/r]+[nt/r].
%C A184815 A184816: 2,5,17,... of the form n+[nr/s]+[nt/s].
%C A184815 A184817: 11,13,19,23,31,... of the form n+[nr/t]+[ns/t].
%C A184815 The Mathematica code can be easily modified to print primes in the three classes.
%H A184815 G. C. Greubel, <a href="/A184815/b184815.txt">Table of n, a(n) for n = 1..5000</a>
%e A184815 See A184812.
%t A184815 r=2^(1/2); s=3^(1/2); t=5^(1/2);
%t A184815 a[n_]:=n+Floor [n*s/r]+Floor[n*t/r];
%t A184815 b[n_]:=n+Floor [n*r/s]+Floor[n*t/s];
%t A184815 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]
%t A184815 Table[a[n],{n,1,120}]  (* A184812 *)
%t A184815 Table[b[n],{n,1,120}]  (* A184813 *)
%t A184815 Table[c[n],{n,1,120}]  (* A184814 *)
%t A184815 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1;
%t A184815 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2;
%t A184815 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,600}];t3
%t A184815 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4;
%t A184815 t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5;
%t A184815 t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,600}];t6
%t A184815 t7={};Do[If[PrimeQ[c[n]], AppendTo[t7,c[n]]],{n,1,600}];t7;
%t A184815 t8={};Do[If[PrimeQ[c[n]], AppendTo[t8,n]],{n,1,600}];t8;
%t A184815 t9={};Do[If[MemberQ[t7,Prime[n]],AppendTo[t9,n]],{n,1,600}];t9
%t A184815 (* Lists t3, t6, t9 match A184815, A184816, A184817. *)
%Y A184815 Cf. A184812, A184816, A184817.
%K A184815 nonn
%O A184815 1,1
%A A184815 _Clark Kimberling_, Jan 23 2011