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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). 4

%I #12 Jan 30 2018 21:45:27

%S 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 63,66,67,73,74,75,77,79,85,87,88,89,94,99,100,102,104,107,110,112,

%U 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 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 See A184812 and A184814.

%H G. C. Greubel, <a href="/A184817/b184817.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. *)

%Y Cf. A184812, A184815, A184816, A184817.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 23 2011

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