cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A373116 Fibonacci numbers whose digits product is a positive perfect power (A001597).

Original entry on oeis.org

1, 8, 55, 144, 4181, 17711, 196418, 1346269, 259695496911122585
Offset: 1

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Author

Gonzalo Martínez, May 25 2024

Keywords

Comments

Since the product of the digits of Fibonacci(k) is required to be positive, Fibonacci(k) does not have zero as a digit. For this reason this list is probably finite, since it is conjectured that there are only finitely many Fibonacci numbers that do not contain the digit zero (see A076564). If the conjecture is true, the largest number possessing the property would be Fibonacci(85) = 259695496911122585 whose digit product is 194400^2.
Unlike A373049, here the product uses all the digits of Fibonacci(k).

Examples

			196418 is a term, because Fibonacci(27) = 196418 and the product of its digits is 1*9*6*4*1*8 = 12^3.

Crossrefs

Cf. A000045, A001597, A076564, A246558, A370071, A373049.

Programs

  • Mathematica
    powQ[n_] := n == 1 || GCD @@ FactorInteger[n][[;; , 2]] > 1; Select[Fibonacci[Range[2, 100]], powQ[Times @@ IntegerDigits[#]] &] (* Amiram Eldar, May 25 2024 *)
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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