A184800 -id:A184800 - cp's OEIS frontend

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

Clark Kimberling, Jan 22 2011

nonn

See A184774.

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

			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,...

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

Cf. A022838. - Bill McEachen, Oct 28 2021

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. *)

A184799 Primes of the form floor(k*s), where s=(3+sqrt(3))/2.

Original entry on oeis.org

2, 7, 11, 23, 37, 47, 59, 61, 73, 89, 97, 101, 113, 127, 137, 139, 149, 151, 163, 167, 179, 191, 227, 229, 241, 257, 269, 281, 283, 293, 307, 317, 331, 347, 359, 373, 383, 397, 409, 421, 449, 461, 463, 487, 499, 503, 541, 563, 577, 593, 617, 619, 631, 641, 643, 653, 683, 709, 719, 733, 757, 761

Offset: 1

Clark Kimberling, Jan 22 2011

nonn

			See A184796.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A184796, A184800, A184801.

filter:= proc(p) local v, k;
  v:= p*(1-1/sqrt(3));
  k:= ceil(v);
  is((v-k+1)^2 > 1/3)
end proc:
select(filter, [seq(ithprime(i),i=1..200)]); # Robert Israel, May 04 2020

Mathematica
```
(See A184796.)
```

A184801 Numbers m such that prime(m) is of the form floor(ks), where s=(3+sqrt(3))/2; complement of A184778.

Original entry on oeis.org

1, 4, 5, 9, 12, 15, 17, 18, 21, 24, 25, 26, 30, 31, 33, 34, 35, 36, 38, 39, 41, 43, 49, 50, 53, 55, 57, 60, 61, 62, 63, 66, 67, 69, 72, 74, 76, 78, 80, 82, 87, 89, 90, 93, 95, 96, 100, 103, 106, 108, 113, 114, 115, 116, 117, 119, 124, 127, 128, 130, 134, 135, 137, 138, 139, 140, 141, 142, 143, 146, 150, 151, 154, 158, 160, 162, 163, 165, 167, 171, 173, 174, 180, 183, 184, 186, 188, 193, 195, 197, 198, 200, 203, 204, 206, 209, 210, 212, 213, 217, 219, 221

Offset: 1

Clark Kimberling, Jan 22 2011

nonn

			See A184796.

A184796, A184797, A184799, A184800.

Mathematica
```
(See A184796.)
```

cp's OEIS Frontend

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

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A184799 Primes of the form floor(k*s), where s=(3+sqrt(3))/2.

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A184801 Numbers m such that prime(m) is of the form floor(ks), where s=(3+sqrt(3))/2; complement of A184778.

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica