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

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

1,1

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

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

Crossrefs

Cf. A000045, A181419, A181393

Sequence in context: A113304 A194945 A093651 * A333291 A254680 A018411

Adjacent sequences: A181417 A181418 A181419 * A181421 A181422 A181423

Keyword

nonn

Author

Vladimir Shevelev, Oct 18 2010

Extensions

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

Status

approved