A184863 Numbers k such that floor(n+nr-r/2) are prime, where r=(1+sqrt(5))/2.

3, 7, 16, 17, 23, 26, 39, 40, 42, 49, 53, 58, 69, 81, 88, 101, 104, 108, 120, 127, 133, 143, 149, 152, 165, 166, 168, 172, 175, 179, 188, 191, 195, 207, 218, 221, 227, 230, 236, 237, 246, 250, 253, 259, 275, 278, 291, 301, 305, 314, 315, 317, 321, 328, 330, 337, 347, 360, 370, 376, 379, 386, 395, 401, 402, 409, 418, 424, 427, 440, 441, 454, 456, 464, 470, 473, 489, 493, 496, 505, 525, 528, 535, 544, 548, 550, 567, 573, 590, 592, 596, 599

Offset: 1

Author

Clark Kimberling, Jan 23 2011

Keywords

• nonn

Crossrefs

Cf. A184862, A184864.

Programs

Mathematica

r=(1+5^(1/2))/2;
a[n_]:=Floor [n+n*r-r/2];
Table[a[n], {n, 1, 120}]  (* A007064 *)
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
*( Lists t1, t2, t3 match A184862, A184863, A184864.)
With[{gr=GoldenRatio},Select[Range[600],PrimeQ[Floor[#+gr*#-gr/2]]&]] (* Harvey P. Dale, Jul 06 2025 *)