A272575 Perfect powers that are the sum of two Fibonacci numbers.

1, 4, 8, 9, 16, 36, 144, 1000, 1600, 14930496

Offset

1,2

Comments

Intersection of A001597 and A084176.

Listed terms are 1, 2^2, 2^3, 3^2, 2^4, 6^2, 12^2, 10^3, 40^2, 3864^2.

First five terms are also members of A000961.

Conjecture: there are no more terms in this sequence. Any remaining terms must have over 10000 digits. - Charles R Greathouse IV, May 04 2016

Links

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

Example

8 is a term because 2^3 = 3 + 5.

Mathematica

Select[Range[10^4], Function[k, Or[k == 1, GCD @@ Map[Last, FactorInteger@ k] > 1] && Total@ Map[Times @@ Boole@ Map[MemberQ[s, #] &, #] &, Transpose@ {#, k - #} &@ Range[0, Floor[k/2]]] > 0]] (* Michael De Vlieger, May 03 2016 *)

Prog

(PARI) list(lim)=my(upper=log(lim*sqrt(5))\log((1+sqrt(5))/2)+1, t, tt, v=List([1])); if(fibonacci(t)>lim, t--); for(i=3, upper, t=fibonacci(i); for(j=2, i-1, tt=t+fibonacci(j); if(tt>lim, break); if(ispower(tt), listput(v, tt)))); Set(v) \\ Charles R Greathouse IV, May 03 2016

Crossrefs

Cf. A000045, A001597, A084176, A111378.

Sequence in context: A089042 A340093 A227243 * A020145 A202271 A334858

Adjacent sequences: A272572 A272573 A272574 * A272576 A272577 A272578

Keyword

nonn

Author

Altug Alkan, May 03 2016

Status

approved