A184802 Primes of the form floor(k*sqrt(5)).

2, 11, 13, 17, 29, 31, 53, 67, 71, 73, 89, 107, 109, 127, 131, 149, 163, 167, 181, 199, 223, 239, 241, 257, 263, 277, 281, 283, 313, 317, 337, 353, 373, 389, 409, 431, 433, 449, 467, 487, 491, 503, 509, 521, 523, 541, 547, 563, 599, 601, 617, 619, 641, 643

Offset: 1

Author

Clark Kimberling, Jan 22 2011

Keywords

• nonn

Comments

See A184774.

Examples

			The sequence U(n)=floor(n*sqrt(5)) begins with
2,4,6,8,11,13,15,17,20,22,24,26,29,...,
which includes the primes U(1)=2, U(5)=11,...
		

Crossrefs

Cf. A184774, A022839, A108598, A184802, A184803, A184804, A184805, A184806, A184807.

Programs

Mathematica

r=5^(1/2); s=r/(r-1);
a[n_]:=Floor [n*r];  (* A022839 *)
b[n_]:=Floor [n*s];  (* A108598 *)
Table[a[n],{n,1,120}]
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,1,300}];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,1,300}];t6
(* The lists t1, t2, t3, t4, t5, t6 match the sequences
A184802, A184803, A184804, A184805, A184806, A184807. *)

PARI

for(k=1,300,isprime(p=sqrtint(k^2*5))&&print1(p",")) \\ M. F. Hasler, Aug 26 2014