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A184859 Primes of the form floor(kr+h), where r=(1+sqrt(5))/2 and h=1/2.

%I A184859 #12 Jul 08 2025 09:25:18
%S A184859 2,3,5,11,13,19,23,29,31,37,47,53,61,71,73,79,83,89,97,107,113,131,
%T A184859 139,149,157,163,167,173,181,191,193,197,199,223,227,233,239,241,251,
%U A184859 257,269,277,283,293,307,311,317,337,349,353,359,367,379,383,401,409,419,421,443,461,463,479,487,503,521,523,547,557,563,571,587,599,607,613,631,641,647,659,673,683,691,701,709,733,739,743,751,757,769,773,809,811,827,853,859,877,883,887,911,919,929,937,947,953,971
%N A184859 Primes of the form floor(kr+h), where r=(1+sqrt(5))/2 and h=1/2.
%C A184859 See "conjecture generalized" at A184774.
%e A184859 The sequence U(n)=floor(n*r+h) begins with
%e A184859 2,3,5,6,8,10,11,13,15,16,18,19,...,
%e A184859 which includes the primes U(1)=2, U(2)=3,...
%t A184859 r=(1+5^(1/2))/2; h=1/2;s=r/(r-1);
%t A184859 a[n_]:=Floor [n*r+h];
%t A184859 Table[a[n],{n,1,120}]  (* A007067 *)
%t A184859 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
%t A184859 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
%t A184859 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
%t A184859 (* Lists t1, t2, t3 match A184859, A184860, A184861. *)
%t A184859 Select[Floor[GoldenRatio*Range[600]+1/2],PrimeQ] (* _Harvey P. Dale_, Jan 02 2013 *)
%Y A184859 Cf. A184774, A184859, A184860, A184861.
%K A184859 nonn
%O A184859 1,1
%A A184859 _Clark Kimberling_, Jan 23 2011