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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

Table of n, a(n) for n=1..97.

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

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

CROSSREFS

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

Sequence in context: A208846 A087723 A299242 * A136998 A136734 A113544

Adjacent sequences:  A184789 A184790 A184791 * A184793 A184794 A184795

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 22 2011

STATUS

approved

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Last modified June 22 17:18 EDT 2021. Contains 345388 sequences. (Running on oeis4.)