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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
OFFSET
1,1
COMMENTS
See A184774.
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
PROG
(PARI) for(k=1, 300, isprime(p=sqrtint(k^2*5))&&print1(p", ")) \\ M. F. Hasler, Aug 26 2014
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 22 2011
STATUS
approved