This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A266960 #18 Nov 15 2020 19:17:03
%S A266960 0,1,2,6,13,356,3126,28691,70268,271396,6534495,64591632,162057126,
%T A266960 26237436541,66438353080,7020479040553,11201604625686,296414282891996,
%U A266960 32360305554728271,339791857819043616,871053578019254406,5731478440138170841,9181907843495831675
%N A266960 Integer averages of first n Fibonacci numbers (beginning with F(0)).
%C A266960 It seems only 0, 1, 2, 13 are Fibonacci numbers.
%C A266960 Are there other Fibonacci numbers of the form (Fibonacci(k) - 1) / (k - 1)?
%C A266960 2 and 13 are the prime numbers. Are there other prime numbers in this sequence?
%F A266960 a(n) = A000071(A219612(n) + 1) / A219612(n).
%e A266960 1 is a term because (Fibonacci(0) + Fibonacci(1) + Fibonacci(2) + Fibonacci(3)) / 4 = 4 / 4 = 1.
%e A266960 2 is a term because (Fibonacci(0) + Fibonacci(1) + Fibonacci(2) + Fibonacci(3) + Fibonacci(4) + Fibonacci(5)) / 6 = 12 / 6 = 2.
%t A266960 Table[Mean@ Fibonacci@ Range[0, n], {n, 0, 100}] /. _Rational -> Nothing (* _Michael De Vlieger_, Jan 07 2016 *)
%t A266960 Module[{nn=100,fibs},fibs=Accumulate[Fibonacci[Range[0,nn]]];Select[ #[[1]] / #[[2]]&/@Thread[{fibs,Range[nn+1]}],IntegerQ]] (* _Harvey P. Dale_, Nov 15 2020 *)
%o A266960 (PARI) m(n) = sum(k=0, n, fibonacci(k)) % (n+1);
%o A266960 b(n) = sum(k=0, n, fibonacci(k)) / (n+1);
%o A266960 for(n=0, 1e2, if(m(n)==0, print1(b(n), ", ")));
%Y A266960 Cf. A101907, A219612.
%K A266960 nonn,easy
%O A266960 1,3
%A A266960 _Altug Alkan_, Jan 07 2016