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A184817 Numbers m such that prime(m) is of the form k+floor(kr/t)+floor(ks/t), where r=sqrt(2), s=sqrt(3), t=sqrt(5).

%I A184817 #12 Jan 30 2018 21:45:27
%S A184817 5,6,8,9,11,15,17,20,25,27,28,31,32,33,35,38,43,46,47,48,51,58,61,62,
%T A184817 63,66,67,73,74,75,77,79,85,87,88,89,94,99,100,102,104,107,110,112,
%U A184817 116,118,120,121,122,127,128,130,132,134,136,141,144,146,147,151,153,154,155,156,163,164,166,167,170,175,177,179,181,184,186,188,194,196,199,201,202,203,204,206,209,210,213,216,218,221,223,225,226,227,228
%N A184817 Numbers m such that prime(m) is of the form k+floor(kr/t)+floor(ks/t), where r=sqrt(2), s=sqrt(3), t=sqrt(5).
%C A184817 See A184812 and A184814.
%H A184817 G. C. Greubel, <a href="/A184817/b184817.txt">Table of n, a(n) for n = 1..5000</a>
%t A184817 r=2^(1/2); s=3^(1/2); t=5^(1/2);
%t A184817 a[n_]:=n+Floor[n*s/r]+Floor[n*t/r];
%t A184817 b[n_]:=n+Floor[n*r/s]+Floor[n*t/s];
%t A184817 c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]
%t A184817 Table[a[n],{n,1,120}]  (* A184812 *)
%t A184817 Table[b[n],{n,1,120}]  (* A184813 *)
%t A184817 Table[c[n],{n,1,120}]  (* A184814 *)
%t A184817 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1;
%t A184817 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2;
%t A184817 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,600}];t3
%t A184817 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4;
%t A184817 t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5;
%t A184817 t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,600}];t6
%t A184817 t7={};Do[If[PrimeQ[c[n]], AppendTo[t7,c[n]]],{n,1,600}];t7;
%t A184817 t8={};Do[If[PrimeQ[c[n]], AppendTo[t8,n]],{n,1,600}];t8;
%t A184817 t9={};Do[If[MemberQ[t7,Prime[n]],AppendTo[t9,n]],{n,1,600}];t9
%t A184817 (* Lists t3, t6, t9 match A184815, A184816, A184817. *)
%Y A184817 Cf. A184812, A184815, A184816, A184817.
%K A184817 nonn
%O A184817 1,1
%A A184817 _Clark Kimberling_, Jan 23 2011