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A181420 Numbers of the form Fibonacci(p^c)/Fibonacci(p^b), where p is some prime and 1<=b are two integer exponents.

%I A181420 #12 Apr 10 2024 03:39:54
%S A181420 3,7,17,21,47,329,987,2207,5777,15005,98209,103729,726103,2178309,
%T A181420 4870847,598364773,10749959329,192900153617,505248088463,
%U A181420 3536736619241,10610209857723,23725150497407,1114384187445409,18944531186571953
%N A181420 Numbers of the form Fibonacci(p^c)/Fibonacci(p^b), where p is some prime and 1<=b<c are two integer exponents.
%C A181420 By inserting dummy factors Fibonacci(p^d)/Fibonacci(p^d) for all intermediate exponents b < d < c it becomes obvious that each entry is a product of factors taken from A181419.
%H A181420 Robert Israel, <a href="/A181420/b181420.txt">Table of n, a(n) for n = 1..125</a>
%p A181420 N:= 10^40: # for terms <= N
%p A181420 S:= {}: p:= 1:
%p A181420 do
%p A181420  p:= nextprime(p);
%p A181420  L:= [combinat:-fibonacci(p)];
%p A181420  for k from 2 do
%p A181420    v:= combinat:-fibonacci(p^k);
%p A181420    if v/L[-1]>N then break fi;
%p A181420    L:= [op(L), v];
%p A181420    for j from k-1 to 1 by -1 do
%p A181420      r:= v/L[j];
%p A181420      if r < N then S:= S union {r} fi;
%p A181420    od;
%p A181420  od;
%p A181420  if k = 2 then break fi;
%p A181420 od:
%p A181420 sort(convert(S,list)); # _Robert Israel_, Apr 09 2024
%Y A181420 Cf. A000045, A181419, A181393
%K A181420 nonn
%O A181420 1,1
%A A181420 _Vladimir Shevelev_, Oct 18 2010
%E A181420 10749959329 inserted by _R. J. Mathar_, Oct 22 2010