A039595 Positive Fibonacci numbers that are also triangular numbers.

1, 3, 21, 55

Offset

1,2

Comments

Vern Hoggatt conjectured and Luo Ming confirmed that these are all the terms. - Tomohiro Yamada, Sep 23 2017

References

Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 55, p. 20, Ellipses, Paris, 2008.

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 275.

Richard K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section D26.

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 28.

David Wells, Curious and interesting numbers, Penguin Books, p. 108.

Links

Table of n, a(n) for n=1..4.

Luo Ming, On Triangular Fibonacci Numbers, Fibonacci Quart. 27 (1989), 98-108.

Mathematica

Union[Select[Fibonacci[Range[20]], OddQ[Sqrt[8#+1]]&]] (* Harvey P. Dale, Jan 17 2015 *)

Crossrefs

Cf. A000045, A000217.

Sequence in context: A303834 A340687 A152773 * A033567 A181156 A356809

Adjacent sequences: A039592 A039593 A039594 * A039596 A039597 A039598

Keyword

nonn,fini,full

Author

Felice Russo

Status

approved