A184865 - OEIS

%I #14 Jan 30 2018 21:45:20

%S 3,7,11,13,17,23,31,37,41,47,59,61,71,79,83,89,103,107,109,113,127,

%T 137,139,151,157,163,167,173,181,191,197,199,211,223,229,233,239,257,

%U 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

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

%C See "conjecture generalized" at A184774.

%H G. C. Greubel, <a href="/A184865/b184865.txt">Table of n, a(n) for n = 1..10000</a>

%t r=2^(1/2); h=1/2; a[n_]:=Floor[n*r+h];

%t Table[a[n],{n,1,120}] (* A022846, int. nearest 2^(1/2) *)

%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 (* Lists t1, t2, t3 match A184865, A184866, A184867. *)

%t Select[Floor[Sqrt[2]Range[1000]+1/2],PrimeQ] (* _Harvey P. Dale_, Oct 31 2011 *)

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

%Y Cf. A184774, A184866, A184867, A184868.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 23 2011