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 A184866 Numbers k such that floor(1/2+k*sqrt(2)) is prime. 3

%I

%S 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 111,115,118,122,128,135,139,141,149,158,162,165,169,182,186,190,196,

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

%H G. C. Greubel, <a href="/A184866/b184866.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. *)

%o (PARI) isok(k) = isprime(floor(1/2+k*sqrt(2))); \\ _Michel Marcus_, Jan 30 2018

%Y Cf. A184865, A184867.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 23 2011

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Last modified April 20 06:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)