cp's OEIS Frontend

A181419 Numbers of the form Fibonacci(p^{k+1})/Fibonacci(p^k) where p are primes, k>=1.

%I A181419 #14 Apr 10 2024 03:38:06
%S A181419 3,7,17,47,2207,5777,15005,4870847,598364773,192900153617,
%T A181419 23725150497407,792070839820228500005,97415813466381445596089,
%U A181419 562882766124611619513723647,400009475456580321242184872389193
%N A181419 Numbers of the form Fibonacci(p^{k+1})/Fibonacci(p^k) where p are primes, k>=1.
%C A181419 The union of A001566 (p=2), A002814 except the first two terms (p=3), A145275 (p=5), A145277 (p=7), etc.
%H A181419 Robert Israel, <a href="/A181419/b181419.txt">Table of n, a(n) for n = 1..44</a>
%p A181419 N:= 10^50: # for terms <= N
%p A181419 S:= {}: p:= 1:
%p A181419 do
%p A181419  p:= nextprime(p);
%p A181419  v:= combinat:-fibonacci(p);
%p A181419  for k from 2 do
%p A181419    w:= v;
%p A181419    v:= combinat:-fibonacci(p^k);
%p A181419    r:= v/w;
%p A181419    if r > N then break fi;
%p A181419    S:= S union {r};
%p A181419  od;
%p A181419  if k = 2 then break fi;
%p A181419 od:
%p A181419 sort(convert(S,list)); # _Robert Israel_, Apr 09 2024
%t A181419 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 *)
%Y A181419 Cf. A001566, A002814, A145275, A145277.
%K A181419 nonn
%O A181419 1,1
%A A181419 _Vladimir Shevelev_, Oct 18 2010
%E A181419 a(11) onwards from _Robert G. Wilson v_, Oct 21 2010