A184815 Numbers m such that prime(m) is of the form k+floor(ks/r)+floor(kt/r), where r=sqrt(2), s=sqrt(3), t=sqrt(5).

2, 4, 10, 12, 13, 16, 22, 29, 30, 36, 42, 44, 45, 49, 52, 57, 59, 60, 64, 70, 71, 76, 82, 84, 90, 91, 92, 97, 101, 103, 108, 111, 114, 115, 119, 123, 125, 138, 140, 142, 149, 150, 165, 171, 178, 180, 182, 185, 189, 191, 192, 193, 195, 198, 205, 211, 215, 217, 220, 222, 224, 233, 235, 236, 247, 248, 249, 252, 254, 255, 264, 265, 269, 273, 286, 295, 301, 302, 306, 307, 309, 316, 318, 325, 326, 327, 328, 329, 332, 336

Offset: 1

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

Comments

A184815, A184816, and A184817 partition the primes:

A184815: 3,7,29,37,... of the form n+[ns/r]+[nt/r].

A184816: 2,5,17,... of the form n+[nr/s]+[nt/s].

A184817: 11,13,19,23,31,... of the form n+[nr/t]+[ns/t].

The Mathematica code can be easily modified to print primes in the three classes.

Examples

			See A184812.
		

Links

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

Crossrefs

Cf. A184812, 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. *)