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.
G = (1 + Sqrt[5])/2; Table[Expand[(G^(4^(n + 1)) - (1 - G)^(4^(n + 1)))/Sqrt[5]]/Expand[(G^(4^n) - (1 - G)^(4^n))/Sqrt[5]], {n, 1, 5}]
G = (1 + Sqrt[5])/2; Table[Expand[(G^(7^(n + 1)) - (1 - G)^(7^(n + 1)))/Sqrt[5]]/Expand[(G^(7^n) - (1 - G)^(7^n))/Sqrt[5]], {n, 1, 5}]
G = (1 + Sqrt[5])/2; Table[Expand[(G^(6^(n + 1)) - (1 - G)^(6^(n + 1)))/Sqrt[5]]/Expand[(G^(6^n) - (1 - G)^(6^n))/Sqrt[5]], {n, 1, 5}]
N:= 10^50: # for terms <= N
S:= {}: p:= 1:
do
p:= nextprime(p);
v:= combinat:-fibonacci(p);
for k from 2 do
w:= v;
v:= combinat:-fibonacci(p^k);
r:= v/w;
if r > N then break fi;
S:= S union {r};
od;
if k = 2 then break fi;
od:
sort(convert(S,list)); # Robert Israel, Apr 09 2024
t = Sort@ Flatten[ Table[ {Prime[n]^(e + 1), Prime[n]^e}, {n, 8}, {e, 10}], 1]; u = Select[t, First@# < 350 &]; Sort[ Fibonacci[ #[[1]]]/Fibonacci[ #[[2]]] & /@ u] (* Robert G. Wilson v, Oct 21 2010 *)
a[n_] := LucasL[4*5^n] - LucasL[2*5^n] + 1; Array[a, 3, 0] (* Amiram Eldar, Jul 20 2025 *)
A219011(n):=fib(5^(n+1))/fib(5^n)$ makelist(A219011(n),n,0,3);
Comments