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

3, 7, 17, 21, 47, 329, 987, 2207, 5777, 15005, 98209, 103729, 726103, 2178309, 4870847, 598364773, 10749959329, 192900153617, 505248088463, 3536736619241, 10610209857723, 23725150497407, 1114384187445409, 18944531186571953

Offset: 1

Author

Vladimir Shevelev, Oct 18 2010

Keywords

• nonn

Comments

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.

Links

• Robert Israel, Table of n, a(n) for n = 1..125

Crossrefs

Cf. A000045, A181419, A181393

Programs

Maple

N:= 10^40: # for terms <= N
S:= {}: p:= 1:
do
 p:= nextprime(p);
 L:= [combinat:-fibonacci(p)];
 for k from 2 do
   v:= combinat:-fibonacci(p^k);
   if v/L[-1]>N then break fi;
   L:= [op(L), v];
   for j from k-1 to 1 by -1 do
     r:= v/L[j];
     if r < N then S:= S union {r} fi;
   od;
 od;
 if k = 2 then break fi;
od:
sort(convert(S,list)); # Robert Israel, Apr 09 2024

Extensions

10749959329 inserted by R. J. Mathar, Oct 22 2010