A184866 Numbers k such that floor(1/2+k*sqrt(2)) is prime.

2, 5, 8, 9, 12, 16, 22, 26, 29, 33, 42, 43, 50, 56, 59, 63, 73, 76, 77, 80, 90, 97, 98, 107, 111, 115, 118, 122, 128, 135, 139, 141, 149, 158, 162, 165, 169, 182, 186, 190, 196, 199, 200, 207, 217, 220, 221, 224, 234, 238, 247, 254, 264, 268, 271, 275, 281, 289, 296, 298, 305, 306, 313, 323, 326, 330, 339, 347, 353, 356, 360, 370, 387, 394, 398, 402, 404, 408, 415, 419, 425, 429, 436, 438, 446, 453, 455, 462, 466, 476, 479, 483, 496, 501, 514, 518, 531, 535, 538, 544, 572, 582, 585, 586, 593

Offset: 1

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A184865, A184867.

Programs

Mathematica

r=2^(1/2); h=1/2; a[n_]:=Floor[n*r+h];
Table[a[n], {n, 1, 120}] (* A022846, int. nearest 2^(1/2) *)
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
(* Lists t1, t2, t3 match A184865, A184866, A184867. *)

PARI

isok(k) = isprime(floor(1/2+k*sqrt(2))); \\ Michel Marcus, Jan 30 2018