A230125 - OEIS

%I #23 Aug 13 2023 07:04:32

%S 55,89,233,377,5702887,9227465,24157817,39088169,7778742049,

%T 86267571272,139583862445,591286729879,956722026041,2504730781961,

%U 4052739537881,61305790721611591,99194853094755497,259695496911122585,420196140727489673,135301852344706746049

%N Fibonacci numbers with no squarefree neighbors.

%C 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

%e 55 is in the sequence because 54 = 2 * 3^3 and 56 = 2^3 * 7 are not squarefree numbers.

%e 89 is in the sequence because 88 = 2^3 * 11 and 90 = 2 * 3^2 * 5 are not squarefree numbers.

%e 144 is not in the sequence because both 143 = 11 * 13 and 145 = 5 * 29 are squarefree.

%p 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

%t Select[Fibonacci[Range[100]], Abs[MoebiusMu[# - 1]] + Abs[MoebiusMu[# + 1]] == 0 &] (* _Alonso del Arte_, Oct 11 2013 *)

%t Select[Fibonacci[Range[100]],NoneTrue[#+{1,-1},SquareFreeQ]&] (* _Harvey P. Dale_, Oct 09 2021 *)

%Y Intersection of A000045 and A281192.

%Y Cf. A005117, A013929.

%K nonn,easy

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 10 2013

%E a(5)-a(20) from _Nathaniel Johnston_, Oct 11 2013