A039595 Positive Fibonacci numbers that are also triangular numbers.

1, 3, 21, 55

Offset: 1

Author

Felice Russo

Keywords

• nonn
• fini
• full

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.
• 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

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

Crossrefs

Cf. A000045, A000217.

Programs

Mathematica

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