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).

5, 6, 8, 9, 11, 15, 17, 20, 25, 27, 28, 31, 32, 33, 35, 38, 43, 46, 47, 48, 51, 58, 61, 62, 63, 66, 67, 73, 74, 75, 77, 79, 85, 87, 88, 89, 94, 99, 100, 102, 104, 107, 110, 112, 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

Offset: 1

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

Comments

See A184812 and A184814.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A184812, A184815, A184816, A184817.

Programs

Mathematica

r=2^(1/2); s=3^(1/2); t=5^(1/2);
a[n_]:=n+Floor[n*s/r]+Floor[n*t/r];
b[n_]:=n+Floor[n*r/s]+Floor[n*t/s];
c[n_]:=n+Floor[n*r/t]+Floor[n*s/t]
Table[a[n],{n,1,120}]  (* A184812 *)
Table[b[n],{n,1,120}]  (* A184813 *)
Table[c[n],{n,1,120}]  (* A184814 *)
t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1;
t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2;
t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,600}];t3
t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4;
t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5;
t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,600}];t6
t7={};Do[If[PrimeQ[c[n]], AppendTo[t7,c[n]]],{n,1,600}];t7;
t8={};Do[If[PrimeQ[c[n]], AppendTo[t8,n]],{n,1,600}];t8;
t9={};Do[If[MemberQ[t7,Prime[n]],AppendTo[t9,n]],{n,1,600}];t9
(* Lists t3, t6, t9 match A184815, A184816, A184817. *)