A258575 Numbers n such that Lucas(n)-Fibonacci(n) is squarefree.

0, 2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 53, 54, 56, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 93, 95, 96, 98, 99, 102, 104, 105

Offset

1,2

Comments

These numbers belong to the sequence A007494 (see Chai Wah Wu argumentation in A258574).

Also numbers n such that 2*Fibonacci(n-1) is squarefree. [Bruno Berselli, Jun 05 2015]

A258575(n) = A258574(n+1)-1. - Chai Wah Wu, Jun 09 2015

Links

Table of n, a(n) for n=1..66.

Mathematica

Select[Range[0, 200], SquareFreeQ[LucasL[#] - Fibonacci[#]] &]

Prog

(Magma) [0] cat [n: n in [2..150] | IsSquarefree(Lucas(n)-Fibonacci(n))];
(Sage) [n for n in (0..110) if is_squarefree(2*fibonacci(n-1))] # Bruno Berselli, Jun 05 2015

Crossrefs

Cf. A000032, A000045, A005117, A007494, A037918, A118658, A258574.

Sequence in context: A294732 A045506 A007494 * A052490 A332076 A248562

Adjacent sequences: A258572 A258573 A258574 * A258576 A258577 A258578

Keyword

nonn,easy,less

Author

Vincenzo Librandi, Jun 04 2015

Extensions

Name corrected by Bruno Berselli, Jun 05 2015

Status

approved