cp's OEIS Frontend

A184796 Primes of the form floor(k*sqrt(3)).

%I A184796 #15 Nov 02 2021 06:31:18
%S A184796 3,5,13,17,19,29,31,41,43,53,67,71,79,83,103,107,109,131,157,173,181,
%T A184796 193,197,199,211,223,233,239,251,263,271,277,311,313,337,349,353,367,
%U A184796 379,389,401,419,431,433,439,443,457,467,479,491,509,521,523,547,557,569,571,587,599,601,607,613,647,659,661,673,677,691,701,727,739,743,751,769,827,829,853,857,859,881,883,907,911,919,937,947,971,983,997,1009,1013,1021,1039
%N A184796 Primes of the form floor(k*sqrt(3)).
%C A184796 See A184774.
%C A184796 Equals the prime terms of A022838. - _Bill McEachen_, Oct 28 2021
%e A184796 The sequence A022838(n)=floor(n*sqrt(3)) begins with 1,3,5,6,8,10,12,13,15,17,19,... which includes the primes A022838(2)=3, A022838(3)=5, A022838(8)=13,...
%t A184796 r=3^(1/2); s=r/(r-1);
%t A184796 a[n_]:=Floor [n*r];  (* A022838 *)
%t A184796 b[n_]:=Floor [n*s];  (* A054406 *)
%t A184796 Table[a[n],{n,1,120}]
%t A184796 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
%t A184796 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
%t A184796 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
%t A184796 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4
%t A184796 t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5
%t A184796 t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6
%t A184796 (* The lists t1, t2, t3, t4, t5, t6 match the sequences
%t A184796 A184796, A184797, A184798, A184799, A184800, A184801. *)
%Y A184796 Cf. A184774, A184797, A184798, A184799, A184800, A184801.
%Y A184796 Cf. A022838. - _Bill McEachen_, Oct 28 2021
%K A184796 nonn
%O A184796 1,1
%A A184796 _Clark Kimberling_, Jan 22 2011