cp's OEIS Frontend

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

%I A184863 #7 Jul 06 2025 13:24:30
%S A184863 3,7,16,17,23,26,39,40,42,49,53,58,69,81,88,101,104,108,120,127,133,
%T A184863 143,149,152,165,166,168,172,175,179,188,191,195,207,218,221,227,230,
%U A184863 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
%N A184863 Numbers k such that floor(n+nr-r/2) are prime, where r=(1+sqrt(5))/2.
%t A184863 r=(1+5^(1/2))/2;
%t A184863 a[n_]:=Floor [n+n*r-r/2];
%t A184863 Table[a[n], {n, 1, 120}]  (* A007064 *)
%t A184863 t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1, a[n]]], {n, 1, 600}]; t1
%t A184863 t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2, n]], {n, 1, 600}]; t2
%t A184863 t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3, n]], {n, 1, 300}]; t3
%t A184863 *( Lists t1, t2, t3 match A184862, A184863, A184864.)
%t A184863 With[{gr=GoldenRatio},Select[Range[600],PrimeQ[Floor[#+gr*#-gr/2]]&]] (* _Harvey P. Dale_, Jul 06 2025 *)
%Y A184863 Cf. A184862, A184864.
%K A184863 nonn
%O A184863 1,1
%A A184863 _Clark Kimberling_, Jan 23 2011