A184810 Numbers m such that prime(m) has the form floor(k*r), where r=sqrt(2/3); complement of A184811.

2, 3, 4, 8, 9, 10, 13, 14, 15, 17, 18, 19, 22, 23, 24, 26, 27, 28, 31, 34, 38, 39, 41, 42, 45, 46, 48, 49, 52, 53, 55, 56, 59, 60, 61, 66, 68, 72, 75, 76, 78, 79, 81, 82, 85, 86, 88, 89, 90, 92, 95, 96, 98, 99, 100, 102, 103, 106, 108, 109, 110, 112, 113, 114, 116, 117, 119, 120, 121, 122, 123, 124, 126, 128, 130, 131, 134, 135, 137, 139, 141, 142, 146, 147, 148, 149, 151, 152, 156, 157, 159, 162, 164, 165, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 180

Offset: 1

Author

Clark Kimberling, Jan 22 2011

Keywords

• nonn

Crossrefs

Cf. A184808, A184809, A184811.

Programs

Mathematica

r=(2/3)^(1/2);s=(3/2)^(1/2); (* complementary because of joint ranking of i*sqrt(2) and j*sqrt(3) *)
a[n_]:=n+Floor [n*r]; b[n_]:=n+Floor [n*s];
Table[a[n],{n,1,120}]  (* A184808 *)
Table[b[n],{n,1,120}]  (* A184809 *)
t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}]
t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}]
t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}]
t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}]
t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6
(* t3 and t6 match A184810 and A184811 *)