A184792 - OEIS

%I #17 Mar 28 2024 15:38:20

%S 2,7,11,12,18,23,27,33,37,38,42,44,49,60,63,64,70,79,81,85,86,101,107,

%T 111,112,122,123,131,138,142,148,149,159,163,168,174,175,190,194,196,

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

%e The sequence L(n)=floor(n*r) begins with

%e 1,3,4,6,8,9,11,12,14,16,17,...,

%e which includes the primes L(2)=3, L(7)=11,...

%t r=(1+5^(1/2))/2; s=r/(r-1);

%t a[n_]:=Floor [n*r];  (* A095280 *)

%t b[n_]:=Floor [n*s];  (* A095281 *)

%t Table[a[n],{n,1,120}]

%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 t4={};Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}];t4

%t t5={};Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}];t5

%t t6={};Do[If[MemberQ[t4,Prime[n]],AppendTo[t6,n]],{n,1,300}];t6

%t (* The lists t1, t2, t3, t4, t5, t6 match the sequences

%t A095280, A184792, A184793, A095281, A184794, A184795 *)

%t Select[Range[600],PrimeQ[Floor[GoldenRatio #]]&] (* _Harvey P. Dale_, Mar 28 2024 *)

%Y Cf. A184774, A095280, A184792, A184793, A095281, A184794, A184795.

%K nonn

%O 1,1

%A _Clark Kimberling_, Jan 22 2011