A184859 Primes of the form floor(kr+h), where r=(1+sqrt(5))/2 and h=1/2.

2, 3, 5, 11, 13, 19, 23, 29, 31, 37, 47, 53, 61, 71, 73, 79, 83, 89, 97, 107, 113, 131, 139, 149, 157, 163, 167, 173, 181, 191, 193, 197, 199, 223, 227, 233, 239, 241, 251, 257, 269, 277, 283, 293, 307, 311, 317, 337, 349, 353, 359, 367, 379, 383, 401, 409, 419, 421, 443, 461, 463, 479, 487, 503, 521, 523, 547, 557, 563, 571, 587, 599, 607, 613, 631, 641, 647, 659, 673, 683, 691, 701, 709, 733, 739, 743, 751, 757, 769, 773, 809, 811, 827, 853, 859, 877, 883, 887, 911, 919, 929, 937, 947, 953, 971

Offset

1,1

Comments

See "conjecture generalized" at A184774.

Links

Table of n, a(n) for n=1..105.

Example

The sequence U(n)=floor(n*r+h) begins with
2,3,5,6,8,10,11,13,15,16,18,19,...,
which includes the primes U(1)=2, U(2)=3,...

Mathematica

r=(1+5^(1/2))/2; h=1/2; s=r/(r-1);
a[n_]:=Floor [n*r+h];
Table[a[n], {n, 1, 120}]  (* A007067 *)
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 A184859, A184860, A184861. *)
Select[Floor[GoldenRatio*Range[600]+1/2], PrimeQ] (* Harvey P. Dale, Jan 02 2013 *)

Crossrefs

Cf. A184774, A184859, A184860, A184861

Sequence in context: A127048 A215370 A139053 * A193213 A153135 A038615

Adjacent sequences: A184856 A184857 A184858 * A184860 A184861 A184862

Keyword

nonn

Author

Clark Kimberling, Jan 23 2011

Status

approved