A275068 - OEIS

%I #12 Nov 19 2024 02:58:36

%S 1,5,11,19,29,31,41,55,59,61,71,79,89,95,101,109,131,139,145,149,151,

%T 155,179,181,191,199,205,209,211,229,239,241,251,269,271,281,295,305,

%U 311,319,331,341,349,355,359,379,389,395,401,409,419,421,431,439,445

%N Squarefree numbers in A022344.

%C The final digit of every number is 1, 5, or 9.  As a set, A022344 consists of the numbers m*F^2, where m is in (1,5,11,19,...) and F is a Fibonacci number.

%H Clark Kimberling, <a href="/A275068/b275068.txt">Table of n, a(n) for n = 0..1000</a>

%e A022344 = (1,5,4,9,16,11,19,11,20,31,19,31,45,29,... ), and deletion of 4,9,16,20, ... leaves (1,5,11,19,29,31,...).

%t g = GoldenRatio; a[n_] := Floor[(n + 1)*g]^2 - n*Floor[(n + 1)*g] - n^2;

%t u = Table[a[n], {n, 0, 200}]  (* A022344 *)

%t Union[Select[u, SquareFreeQ[#] &]]  (* A275068 *)

%Y Cf. A000045, A022344.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jul 15 2016