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

3, 5, 13, 17, 19, 29, 31, 41, 43, 53, 67, 71, 79, 83, 103, 107, 109, 131, 157, 173, 181, 193, 197, 199, 211, 223, 233, 239, 251, 263, 271, 277, 311, 313, 337, 349, 353, 367, 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

Offset

1,1

Comments

See A184774.

Equals the prime terms of A022838. - Bill McEachen, Oct 28 2021

Links

Table of n, a(n) for n=1..93.

Example

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,...

Mathematica

r=3^(1/2); s=r/(r-1);
a[n_]:=Floor [n*r];  (* A022838 *)
b[n_]:=Floor [n*s];  (* A054406 *)
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
A184796, A184797, A184798, A184799, A184800, A184801. *)

Crossrefs

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

Cf. A022838. - Bill McEachen, Oct 28 2021

Sequence in context: A018329 A090545 A045411 * A180944 A049282 A003625

Adjacent sequences: A184793 A184794 A184795 * A184797 A184798 A184799

Keyword

nonn

Author

Clark Kimberling, Jan 22 2011

Status

approved