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

Author

Juri-Stepan Gerasimov, Oct 10 2013

Keywords

• nonn
• easy

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

Examples

			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.
		

Crossrefs

Intersection of A000045 and A281192.

Cf. A005117, A013929.

Programs

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 *)

Extensions

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