A291673 Padovan numbers that are also Fibonacci numbers.

0, 1, 2, 3, 5, 21

Offset

1,3

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

Table of n, a(n) for n=1..6.

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.

Mathematica

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

Crossrefs

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

Sequence in context: A184252 A228833 A320950 * A076383 A024766 A058959

Adjacent sequences: A291670 A291671 A291672 * A291674 A291675 A291676

Keyword

nonn,more

Author

Hugo Pfoertner, Aug 29 2017

Status

approved