A061305 - OEIS

%I #39 Oct 27 2023 22:05:37

%S 1,1,2,3,5,13,21,34,55,89,233,377,610,987,1597,4181,6765,10946,17711,

%T 28657,121393,196418,317811,514229,1346269,2178309,3524578,5702887,

%U 9227465,24157817,39088169,63245986,102334155,165580141,433494437,701408733,1134903170,1836311903

%N Squarefree Fibonacci numbers.

%C Union of A074691 and A075735. - _R. J. Mathar_, Feb 06 2010

%C About 60% of entries are of the form 4k+1; 20% are of the form 4k+2; 20% are of the form 4k+3. Obviously no term is divisible by 4. - _Carmine Suriano_, Feb 27 2014

%C Contains A030426 as a subsequence unless there exist Wall-Sun-Sun primes. - _Max Alekseyev_, Jan 04 2018

%H Amiram Eldar, <a href="/A061305/b061305.txt">Table of n, a(n) for n = 1..1080</a> (terms 1..200 from Zak Seidov)

%F Set difference of A000045 and A061899. a(n) = A000045(A037918(n)). - _R. J. Mathar_, Feb 16 2010

%e 55 = 5 * 11 is a squarefree Fibonacci number.

%t a={}; Do[f=Fibonacci[n]; If[SquareFreeQ[f], AppendTo[a, f]], {n, 1, 50}]; a (* _Vladimir Joseph Stephan Orlovsky_, Jul 22 2008 *)

%t Select[Fibonacci[Range[50]],SquareFreeQ] (* _Harvey P. Dale_, Aug 26 2021 *)

%o (PARI) { n=0; g=0; f=1; for (i=1, 500, if (issquarefree(g), write("b061305.txt", n++, " ", g)); if (n==200, break); s=f; f+=g; g=s ) } \\ _Harry J. Smith_, Jul 21 2009

%Y Intersection of A000045 and A005117.

%K nonn,easy

%O 1,3

%A _Amarnath Murthy_, Apr 26 2001

%E More terms from _Asher Auel_, May 14 2001

%E Mathematica updated by _Jean-François Alcover_, Jul 04 2013