A382869 - OEIS

%I #10 Apr 13 2025 16:19:53

%S 1,2,3,4,7,9,11,1751,2031,45012,105772,1266256,1490601,1774525

%N Numbers k >= 1 such that A018804(k) is a Fibonacci number (A000045).

%e For k = 4: A018804(4) = 8, 8 is a Fibonacci number, thus 4 is a term.

%t fibQ[n_] := Or @@ IntegerQ /@ Sqrt[5*n^2 + {-4, 4}]; f[p_, e_] := (e*(p - 1)/p + 1)*p^e; q[n_] := fibQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[120000], q] (* _Amiram Eldar_, Apr 07 2025 *)

%Y Cf. A000045, A018804.

%Y Similar sequence : A005382.

%K nonn,more

%O 1,2

%A _Ctibor O. Zizka_, Apr 07 2025

%E a(10)-a(14) from _Amiram Eldar_, Apr 07 2025