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A184802 Primes of the form floor(k*sqrt(5)). 6
2, 11, 13, 17, 29, 31, 53, 67, 71, 73, 89, 107, 109, 127, 131, 149, 163, 167, 181, 199, 223, 239, 241, 257, 263, 277, 281, 283, 313, 317, 337, 353, 373, 389, 409, 431, 433, 449, 467, 487, 491, 503, 509, 521, 523, 541, 547, 563, 599, 601, 617, 619, 641, 643 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A184774.

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

The sequence U(n)=floor(n*sqrt(5)) begins with

2,4,6,8,11,13,15,17,20,22,24,26,29,...,

which includes the primes U(1)=2, U(5)=11,...

MATHEMATICA

r=5^(1/2); s=r/(r-1);

a[n_]:=Floor [n*r];  (* A022839 *)

b[n_]:=Floor [n*s];  (* A108598 *)

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

A184802, A184803, A184804, A184805, A184806, A184807. *)

PROG

(PARI) for(k=1, 300, isprime(p=sqrtint(k^2*5))&&print1(p", ")) \\ M. F. Hasler, Aug 26 2014

CROSSREFS

Cf. A184774, A022839, A108598, A184802, A184803, A184804, A184805, A184806, A184807.

Sequence in context: A141168 A259394 A079132 * A023257 A178796 A068807

Adjacent sequences:  A184799 A184800 A184801 * A184803 A184804 A184805

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 22 2011

STATUS

approved

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Last modified May 26 15:29 EDT 2019. Contains 323597 sequences. (Running on oeis4.)