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A184792 Numbers k such that floor(k*r) is prime, where r = golden ratio=(1+sqrt(5))/2.

%I A184792 #17 Mar 28 2024 15:38:20
%S A184792 2,7,11,12,18,23,27,33,37,38,42,44,49,60,63,64,70,79,81,85,86,101,107,
%T A184792 111,112,122,123,131,138,142,148,149,159,163,168,174,175,190,194,196,
%U A184792 205,215,216,222,227,231,237,241,248,253,259,268,274,278,283,285,289,301,304,309,311,315,322,348,352,353,357,363,367,372,379,383,390,398,400,404,409,416,419,457,468,478,487,493,500,508,509,519,530,531,545,546,561,568,582,589,598
%N A184792 Numbers k such that floor(k*r) is prime, where r = golden ratio=(1+sqrt(5))/2.
%e A184792 The sequence L(n)=floor(n*r) begins with
%e A184792 1,3,4,6,8,9,11,12,14,16,17,...,
%e A184792 which includes the primes L(2)=3, L(7)=11,...
%t A184792 r=(1+5^(1/2))/2; s=r/(r-1);
%t A184792 a[n_]:=Floor [n*r];  (* A095280 *)
%t A184792 b[n_]:=Floor [n*s];  (* A095281 *)
%t A184792 Table[a[n],{n,1,120}]
%t A184792 t1={};Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
%t A184792 t2={};Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
%t A184792 t3={};Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
%t A184792 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4
%t A184792 t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5
%t A184792 t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6
%t A184792 (* The lists t1, t2, t3, t4, t5, t6 match the sequences
%t A184792 A095280, A184792, A184793, A095281, A184794, A184795 *)
%t A184792 Select[Range[600],PrimeQ[Floor[GoldenRatio #]]&] (* _Harvey P. Dale_, Mar 28 2024 *)
%Y A184792 Cf. A184774, A095280, A184792, A184793, A095281, A184794, A184795.
%K A184792 nonn
%O A184792 1,1
%A A184792 _Clark Kimberling_, Jan 22 2011