A184816 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).

1, 3, 7, 14, 18, 19, 21, 23, 24, 26, 34, 37, 39, 40, 41, 50, 53, 54, 55, 56, 65, 68, 69, 72, 78, 80, 81, 83, 86, 93, 95, 96, 98, 105, 106, 109, 113, 117, 124, 126, 129, 131, 133, 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

Offset: 1

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

Comments

See A184812 and A184815.

Links

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

Crossrefs

Cf. A184812, A184815, 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. *)
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 *)