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

%I A184866 #10 Jan 30 2018 21:45:12
%S A184866 2,5,8,9,12,16,22,26,29,33,42,43,50,56,59,63,73,76,77,80,90,97,98,107,
%T A184866 111,115,118,122,128,135,139,141,149,158,162,165,169,182,186,190,196,
%U A184866 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
%N A184866 Numbers k such that floor(1/2+k*sqrt(2)) is prime.
%H A184866 G. C. Greubel, <a href="/A184866/b184866.txt">Table of n, a(n) for n = 1..10000</a>
%t A184866 r=2^(1/2); h=1/2; a[n_]:=Floor[n*r+h];
%t A184866 Table[a[n], {n, 1, 120}] (* A022846, int. nearest 2^(1/2) *)
%t A184866 t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1, a[n]]], {n, 1, 600}]; t1
%t A184866 t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2, n]], {n, 1, 600}]; t2
%t A184866 t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3, n]], {n, 1, 300}]; t3
%t A184866 (* Lists t1, t2, t3 match A184865, A184866, A184867. *)
%o A184866 (PARI) isok(k) = isprime(floor(1/2+k*sqrt(2))); \\ _Michel Marcus_, Jan 30 2018
%Y A184866 Cf. A184865, A184867.
%K A184866 nonn
%O A184866 1,1
%A A184866 _Clark Kimberling_, Jan 23 2011