cp's OEIS Frontend

A184862 Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2.

%I A184862 #7 Sep 18 2024 19:41:31
%S A184862 7,17,41,43,59,67,101,103,109,127,137,151,179,211,229,263,271,281,313,
%T A184862 331,347,373,389,397,431,433,439,449,457,467,491,499,509,541,569,577,
%U A184862 593,601,617,619,643,653,661,677,719,727,761,787,797,821,823,829,839,857,863,881,907,941,967,983,991,1009,1033,1049,1051,1069,1093,1109,1117,1151,1153,1187,1193,1213,1229,1237,1279,1289,1297,1321,1373,1381,1399,1423,1433,1439,1483,1499,1543,1549,1559,1567
%N A184862 Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2.
%C A184862 See "conjecture generalized" at A184774.
%t A184862 r=(1+5^(1/2))/2;
%t A184862 a[n_]:=Floor [n+n*r-r/2];
%t A184862 Table[a[n],{n,1,120}]  (* A007064 *)
%t A184862 t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]],{n,1,600}];t1
%t A184862 t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]],{n,1,600}];t2
%t A184862 t3={}; Do[If[MemberQ[t1,Prime[n]],AppendTo[t3,n]],{n,1,300}];t3
%t A184862 *( Lists t1, t2, t3 match A184862, A184863, A184864.)
%t A184862 With[{gr=GoldenRatio},Select[Table[Floor[n+n*gr-gr/2],{n,2000}],PrimeQ]] (* _Harvey P. Dale_, Sep 18 2024 *)
%Y A184862 Cf. A007064, A184774, A184859, A184863, A184864.
%K A184862 nonn
%O A184862 1,1
%A A184862 _Clark Kimberling_, Jan 23 2011