A291216 -id:A291216 - cp's OEIS frontend

A100891 Prime Padovan numbers.

2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719

Offset: 1

John Lien, Jan 10 2005

nonn

Next term corresponds to Padovan(1262) and has 154 decimal digits.

Midhat J. Gazale, "Gnomon: From Pharaohs to Fractals", Princeton University Press, 1999.

Hugo Pfoertner, Table of n, a(n) for n = 1..20
Ian Stewart, Tales of a Neglected Number.
Eric Weisstein's World of Mathematics, Padovan Sequence

Cf. A000931, A122498, A291216, A291673.

Indices of prime Padovan numbers are A112882.

Rest[Select[LinearRecurrence[{0,1,1},{1,1,2},1000],PrimeQ]] (* Harvey P. Dale, Mar 31 2012 *)

More terms from Robert G. Wilson v, Jan 14 2005

A291673 Padovan numbers that are also Fibonacci numbers.

Original entry on oeis.org

0, 1, 2, 3, 5, 21

Offset: 1

Hugo Pfoertner, Aug 29 2017

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

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.

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

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

cp's OEIS Frontend

A100891 Prime Padovan numbers.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Extensions