A075738 Squarefree Fibonacci numbers whose indices are also squarefree.

1, 1, 2, 5, 13, 55, 89, 233, 377, 610, 1597, 4181, 10946, 17711, 28657, 121393, 514229, 1346269, 3524578, 5702887, 9227465, 24157817, 39088169, 63245986, 165580141, 433494437, 1836311903, 2971215073, 20365011074, 53316291173

Offset

1,3

Links

Table of n, a(n) for n=1..30.

Example

Fib(10)=55 is there because both 10 and 55 are squarefree.

Maple

with(combinat, fibonacci): fib_supM_dsk := proc(n); if (numtheory[issqrfree](n)='true') then if (numtheory[issqrfree](fibonacci(n))='true') then RETURN(fibonacci(n)); fi; fi; end: seq(fib_supM_dsk(i), i=1..100);

Mathematica

Select[With[{nn=70}, Thread[{Range[nn], Fibonacci[Range[nn]]}]], AllTrue[#, SquareFreeQ]&][[All, 2]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 17 2018 *)

Crossrefs

Cf. A000045, A005117, A061305, A075739.

Sequence in context: A105905 A236513 A214853 * A076999 A360507 A306827

Adjacent sequences: A075735 A075736 A075737 * A075739 A075740 A075741

Keyword

easy,nonn

Author

Jani Melik, Oct 07 2002

Extensions

Edited by Don Reble, Nov 05 2005

Status

approved