A230125 Fibonacci numbers with no squarefree neighbors.

55, 89, 233, 377, 5702887, 9227465, 24157817, 39088169, 7778742049, 86267571272, 139583862445, 591286729879, 956722026041, 2504730781961, 4052739537881, 61305790721611591, 99194853094755497, 259695496911122585, 420196140727489673, 135301852344706746049

Offset

1,1

Comments

First even term is the 54th Fibonacci number. The next even term is 927372692193078999176, which is the 102nd Fibonacci number. - Alonso del Arte, Oct 11 2013

Links

Table of n, a(n) for n=1..20.

Example

55 is in the sequence because 54 = 2 * 3^3 and 56 = 2^3 * 7 are not squarefree numbers.
89 is in the sequence because 88 = 2^3 * 11 and 90 = 2 * 3^2 * 5 are not squarefree numbers.
144 is not in the sequence because both 143 = 11 * 13 and 145 = 5 * 29 are squarefree.

Maple

issqrfreeneigh := proc(n) return not (issqrfree(m-1) or issqrfree(m+1)): end proc: for n from 1 to 100 do m:=combinat[fibonacci](n): if issqrfreeneigh(m) then printf("%d, ", m): end if: end do: # Nathaniel Johnston, Oct 11 2013

Mathematica

Select[Fibonacci[Range[100]], Abs[MoebiusMu[# - 1]] + Abs[MoebiusMu[# + 1]] == 0 &] (* Alonso del Arte, Oct 11 2013 *)
Select[Fibonacci[Range[100]], NoneTrue[#+{1, -1}, SquareFreeQ]&] (* Harvey P. Dale, Oct 09 2021 *)

Crossrefs

Intersection of A000045 and A281192.

Cf. A005117, A013929.

Sequence in context: A320507 A039533 A157484 * A027865 A247681 A195118

Adjacent sequences: A230122 A230123 A230124 * A230126 A230127 A230128

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Oct 10 2013

Extensions

a(5)-a(20) from Nathaniel Johnston, Oct 11 2013

Status

approved