A184792 Numbers k such that floor(k*r) is prime, where r = golden ratio=(1+sqrt(5))/2.
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
Offset: 1
Keywords
Examples
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,...
Programs
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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 *) Select[Range[600],PrimeQ[Floor[GoldenRatio #]]&] (* Harvey P. Dale, Mar 28 2024 *)