OFFSET

1,3

COMMENTS

For most of the terms in this list, the product of their nonzero digits is a perfect square.

Conjecture: this sequence has infinitely many terms. Since the product of the nonzero digits of Fibonacci(k) is of the form 2^a * 3^b * 5^c * 7^d, a sufficient condition for Fibonacci(k) to belong to the sequence is that a, b, c and d are all even.

EXAMPLE

21 is a term, because Fibonacci(21) = 10946 and the product of its nonzero digits is 1*9*4*6 = 6^3.

46 is a term, because Fibonacci(46) = 1836311903 and the product of its nonzero digits is 1*8*3*6*3*1*1*9*3 = 108^2.

MATHEMATICA

powQ[n_] := n == 1 || GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Range[0, 700], powQ[Times @@ Select[IntegerDigits[Fibonacci[#]], #1 > 0 &]] &] (* Amiram Eldar, May 25 2024 *)

PROG

(PARI) isok(k) = my(x=vecprod(select(x->(x>0), digits(fibonacci(k))))); (x==1) || ispower(x); \\ Michel Marcus, May 20 2024

CROSSREFS

KEYWORD

nonn,base

AUTHOR

Gonzalo MartÃnez, May 20 2024

EXTENSIONS

More terms from Michel Marcus, May 20 2024

STATUS

approved