A118728 - OEIS

A118728

a(n) = smallest squarefree number not less than a(n-1)+a(n-2), a(1)=1, a(0)=0.

%I #18 Dec 10 2024 08:58:48

%S 0,1,2,3,5,10,15,26,41,67,109,177,286,463,749,1213,1963,3178,5141,

%T 8319,13461,21781,35242,57023,92265,149289,241554,390845,632399,

%U 1023245,1655645,2678890,4334537,7013427,11347966,18361393,29709359

%N a(n) = smallest squarefree number not less than a(n-1)+a(n-2), a(1)=1, a(0)=0.

%H Vincenzo Librandi, <a href="/A118728/b118728.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = A067535*(a(n-2)+a(n-1)) for n>1.

%t Module[{lst={0,1}},Do[Module[{k=Total[Take[lst,-2]]}, While[!SquareFreeQ[ k], k++];AppendTo[lst,k]],{40}];Join[{0},Drop[lst,2]]] (* _Harvey P. Dale_, May 16 2012 *)

%t ssn[{a_,b_}]:=Module[{k=a+b},While[!SquareFreeQ[k],k++];k]; Join[{0},Drop[NestList[ {#[[2]],ssn[#]}&,{0,1},40][[;;,1]],2]] (* _Harvey P. Dale_, Aug 12 2024 *)

%Y Cf. A000045, A005117.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, May 21 2006