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A184792 Numbers k such that floor(k*r) is prime, where r = golden ratio=(1+sqrt(5))/2. 5
2, 7, 11, 12, 18, 23, 27, 33, 37, 38, 42, 44, 49, 60, 63, 64, 70, 79, 81, 85, 86, 101, 107, 111, 112, 122, 123, 131, 138, 142, 148, 149, 159, 163, 168, 174, 175, 190, 194, 196, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A087723 A359167 A299242 * A136998 A136734 A113544
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 22 2011
STATUS
approved

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Last modified April 12 20:38 EDT 2024. Contains 371639 sequences. (Running on oeis4.)