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%I #11 Apr 25 2023 14:54:46
%S 1,3,7,14,18,19,21,23,24,26,34,37,39,40,41,50,53,54,55,56,65,68,69,72,
%T 78,80,81,83,86,93,95,96,98,105,106,109,113,117,124,126,129,131,133,
%U 135,137,139,143,145,148,152,157,158,159,160,161,162,168,169,172,173,174,176,183,187,190,197,200,207,208,212,214,219,229,232,234,238,242,243,245,246,257,258,259,266,267,268,270,275,276,278,279,280,281,284
%N Numbers m such that prime(m) is of the form k+floor(kr/s)+floor(kt/s), where r=sqrt(2), s=sqrt(3), t=sqrt(5).
%C See A184812 and A184815.
%H G. C. Greubel, <a href="/A184816/b184816.txt">Table of n, a(n) for n = 1..5000</a>
%t r=2^(1/2); s=3^(1/2); t=5^(1/2);
%t a[n_]:=n+Floor[n*s/r]+Floor[n*t/r];
%t b[n_]:=n+Floor[n*r/s]+Floor[n*t/s];
%t c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]
%t Table[a[n],{n,1,120}] (* A184812 *)
%t Table[b[n],{n,1,120}] (* A184813 *)
%t Table[c[n],{n,1,120}] (* A184814 *)
%t t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1;
%t t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2;
%t t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,600}];t3
%t t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4;
%t t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5;
%t t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,600}];t6
%t t7={};Do[If[PrimeQ[c[n]], AppendTo[t7,c[n]]],{n,1,600}];t7;
%t t8={};Do[If[PrimeQ[c[n]], AppendTo[t8,n]],{n,1,600}];t8;
%t t9={};Do[If[MemberQ[t7,Prime[n]],AppendTo[t9,n]],{n,1,600}];t9
%t (* Lists t3, t6, t9 match A184815, A184816, A184817. *)
%t PrimePi/@Select[Table[k+Floor[(k Sqrt[2])/Sqrt[3]]+Floor[(k Sqrt[5])/Sqrt[3]],{k,600}],PrimeQ] (* _Harvey P. Dale_, Apr 25 2023 *)
%Y Cf. A184812, A184815, A184817.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 23 2011
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