A184796 - OEIS

%I #15 Nov 02 2021 06:31:18

%S 3,5,13,17,19,29,31,41,43,53,67,71,79,83,103,107,109,131,157,173,181,

%T 193,197,199,211,223,233,239,251,263,271,277,311,313,337,349,353,367,

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

%C See A184774.

%C Equals the prime terms of A022838. - _Bill McEachen_, Oct 28 2021

%e 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 r=3^(1/2); s=r/(r-1);

%t a[n_]:=Floor [n*r];  (* A022838 *)

%t b[n_]:=Floor [n*s];  (* A054406 *)

%t Table[a[n],{n,1,120}]

%t t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1

%t t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2

%t t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3

%t t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4

%t t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5

%t t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6

%t (* The lists t1, t2, t3, t4, t5, t6 match the sequences

%t A184796, A184797, A184798, A184799, A184800, A184801. *)

%Y Cf. A184774, A184797, A184798, A184799, A184800, A184801.

%Y Cf. A022838. - _Bill McEachen_, Oct 28 2021

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 22 2011