A277213 Least k such that Fibonacci(k + 1) has n times as many distinct prime factors as Fibonacci(k), or 0 if no such k exists.

3, 7, 17, 23, 29, 47, 167, 419, 83

Offset

1,1

Comments

Least k such that A001221(Fibonacci(k+1)) / A001221(Fibonacci(k)) = n, or 0 if no such k exists.

Links

Table of n, a(n) for n=1..9.

Example

a(2) = 7 because Fibonacci(8) = 21 = 3*7 (2 distinct prime factors) and Fibonacci(7) = 13 (1 prime factor), and 2/1 is 2.

Mathematica

Flatten[Table[Position[Partition[PrimeNu[Fibonacci[Range[2, 420]]], 2, 1], _?(k #[[1]]==#[[2]]&), 1, 1, Heads->False], {k, 9}]]+1 (* Harvey P. Dale, Jan 31 2025 *)

Crossrefs

Cf. A000045, A001221, A022307, A277207.

Sequence in context: A018411 A083989 A374482 * A152451 A097958 A118940

Adjacent sequences: A277210 A277211 A277212 * A277214 A277215 A277216

Keyword

nonn,more

Author

Altug Alkan, Oct 05 2016

Extensions

a(8)-a(9) from Charles R Greathouse IV, Oct 05 2016

Status

approved