A184865 Primes of the form floor(nr+h), where r=sqrt(2), h=1/2.

3, 7, 11, 13, 17, 23, 31, 37, 41, 47, 59, 61, 71, 79, 83, 89, 103, 107, 109, 113, 127, 137, 139, 151, 157, 163, 167, 173, 181, 191, 197, 199, 211, 223, 229, 233, 239, 257, 263, 269, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 349, 359, 373, 379, 383, 389, 397, 409, 419, 421, 431, 433, 443, 457, 461, 467, 479, 491, 499, 503, 509, 523, 547, 557, 563, 569, 571, 577, 587, 593, 601, 607, 617, 619, 631, 641, 643, 653, 659, 673, 677, 683, 701, 709, 727, 733, 751, 757, 761, 769, 809, 823, 827, 829, 839

Offset

1,1

Comments

See "conjecture generalized" at A184774.

Links

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

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. *)
Select[Floor[Sqrt[2]Range[1000]+1/2], PrimeQ] (* Harvey P. Dale, Oct 31 2011 *)

Prog

(PARI) lista(nn) = for (k=1, nn, if (isprime(p=floor(1/2+k*sqrt(2))), print1(p, ", "))); \\ Michel Marcus, Jan 30 2018

Crossrefs

Cf. A184774, A184866, A184867, A184868.

Sequence in context: A310196 A020574 A020618 * A055211 A183176 A045417

Adjacent sequences: A184862 A184863 A184864 * A184866 A184867 A184868

Keyword

nonn

Author

Clark Kimberling, Jan 23 2011

Status

approved