cp's OEIS Frontend

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

%I A184802 #12 Aug 27 2014 10:02:36
%S A184802 2,11,13,17,29,31,53,67,71,73,89,107,109,127,131,149,163,167,181,199,
%T A184802 223,239,241,257,263,277,281,283,313,317,337,353,373,389,409,431,433,
%U A184802 449,467,487,491,503,509,521,523,541,547,563,599,601,617,619,641,643
%N A184802 Primes of the form floor(k*sqrt(5)).
%C A184802 See A184774.
%e A184802 The sequence U(n)=floor(n*sqrt(5)) begins with
%e A184802 2,4,6,8,11,13,15,17,20,22,24,26,29,...,
%e A184802 which includes the primes U(1)=2, U(5)=11,...
%t A184802 r=5^(1/2); s=r/(r-1);
%t A184802 a[n_]:=Floor [n*r];  (* A022839 *)
%t A184802 b[n_]:=Floor [n*s];  (* A108598 *)
%t A184802 Table[a[n],{n,1,120}]
%t A184802 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
%t A184802 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
%t A184802 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
%t A184802 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4
%t A184802 t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5
%t A184802 t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6
%t A184802 (* The lists t1, t2, t3, t4, t5, t6 match the sequences
%t A184802 A184802, A184803, A184804, A184805, A184806, A184807. *)
%o A184802 (PARI) for(k=1,300,isprime(p=sqrtint(k^2*5))&&print1(p",")) \\ _M. F. Hasler_, Aug 26 2014
%Y A184802 Cf. A184774, A022839, A108598, A184802, A184803, A184804, A184805, A184806, A184807.
%K A184802 nonn
%O A184802 1,1
%A A184802 _Clark Kimberling_, Jan 22 2011