OFFSET
1,1
EXAMPLE
The sequence L(n)=floor(n*r) begins with
1,3,4,6,8,9,11,12,14,16,17,...,
which includes the primes L(2)=3, L(7)=11,...
MATHEMATICA
r=(1+5^(1/2))/2; s=r/(r-1);
a[n_]:=Floor [n*r]; (* A095280 *)
b[n_]:=Floor [n*s]; (* A095281 *)
Table[a[n], {n, 1, 120}]
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1, a[n]]], {n, 1, 600}]; t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2, n]], {n, 1, 600}]; t2
t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3, n]], {n, 1, 300}]; t3
t4={}; Do[If[PrimeQ[b[n]], AppendTo[t4, b[n]]], {n, 1, 600}]; t4
t5={}; Do[If[PrimeQ[b[n]], AppendTo[t5, n]], {n, 1, 600}]; t5
t6={}; Do[If[MemberQ[t4, Prime[n]], AppendTo[t6, n]], {n, 1, 300}]; t6
(* The lists t1, t2, t3, t4, t5, t6 match the sequences
Select[Range[600], PrimeQ[Floor[GoldenRatio #]]&] (* Harvey P. Dale, Mar 28 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 22 2011
STATUS
approved