A272712 Perfect powers that are the difference of two nonnegative Fibonacci numbers.

1, 4, 8, 16, 32, 81, 144, 225, 343, 576

Offset

1,2

Comments

Listed 10 terms are 1, 2^2, 2^3, 2^4, 2^5, 3^4, 12^2, 15^2, 3^5, 24^2.

1, 4, 8, 16, 32, 81, 343 are also members of A000961.

1, 4, 8, 16, 144 are in the intersection of this sequence and A272575.

Is this sequence finite?

If a(11) exists, it must be larger than 10^2000. - Giovanni Resta, May 25 2016

Links

Table of n, a(n) for n=1..10.

Example

32 is a term because 32 = 2^5 = 34 - 2 = Fibonacci(9) - Fibonacci(3).

Maple

isA272712 := proc(n)
    isA001597(n) and isA007298(n) ; #uses code in A001597 and A007298
end proc:
for n from 1 do
    if isA272712(n) then
        printf("%d\n", n) ;
    end if;
end do: # R. J. Mathar, May 25 2016

Mathematica

isA001597[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1;
isA007298[n_] := Module[{i, Fi, j, Fj}, For[i = 0, True, i++, Fi = Fibonacci[i]; For[j = i, True, j++, Fj = Fibonacci[j]; Which[Fj - Fi == n, Return@True, Fj - Fi > n, Break[]]]; Fj := Fibonacci[i + 1]; If[Fj - Fi > n, Return@False]]];
Select[Range[1000], isA001597[#] && isA007298[#]&] (* Jean-François Alcover, Nov 16 2023, after R. J. Mathar in A007298 *)

Crossrefs

Cf. A000961, A007298, A001597, A219114, A272575.

Sequence in context: A089890 A338313 A049932 * A020161 A068890 A073856

Adjacent sequences: A272709 A272710 A272711 * A272713 A272714 A272715

Keyword

nonn,more

Author

Altug Alkan, May 05 2016

Status

approved