A291673 Padovan numbers that are also Fibonacci numbers.

0, 1, 2, 3, 5, 21

Offset: 1

Author

Hugo Pfoertner, Aug 29 2017

Keywords

• nonn
• more

Comments

Common terms of A000931 and A000045.

Cited from Ian Stewart's article "Tales of a Neglected Number": "Some numbers, such as 3, 5 and 21, are both Fibonacci and Padovan. Are there others?"

In the b-files provided for both sequences, no further matches are found.

No other terms < 10^(10^5). - Chai Wah Wu, Aug 29 2017

Links

• Ian Stewart, Tales of a Neglected Number, Mathematical Recreations, Scientific American, June 1996.
• Ian Stewart, Die unscheinbare Schwester der goldenen Zahl, Spektrum der Wissenschaft, Dossier 02/2003: Mathematische Unterhaltungen II, 55-57.

Crossrefs

Cf. A000045, A000931, A100891, A122498, A291216.

Programs

Mathematica

With[{nn=100},Join[{0},Intersection[LinearRecurrence[{0,1,1},{1,1,2},nn],Fibonacci[Range[nn]]]]] (* Harvey P. Dale, Oct 09 2017 *)