A248506 Lucas numbers that are also triangular numbers.

1, 3, 5778

Offset: 1

Author

Vincenzo Librandi, Dec 06 2014

Keywords

• nonn
• fini
• full
• bref

Comments

Intersection of A000032 and A000217.

All terms are shown, see Theorem 1.1 in the Tengely reference. - Joerg Arndt, Dec 06 2014

Examples

			Lucas(18) = 5778 = 107*108/2.
		

References

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

Links

• Luo Ming, On Triangular Fibonacci Numbers, The Fibonacci Quarterly, 27.2 (1989), pp. 98-108.
• Luo Ming, On Triangular Lucas Numbers, Applications of Fibonacci Numbers, 1991, pp 231-240.
• Szabolcs Tengely, Finding g-gonal numbers in recurrence sequences, Fibonacci Quarterly, vol.46/47, no.3, pp.235-240, (2009).

Crossrefs

Cf. A000032, A000217, A039595.

Programs

Mathematica

Select[LucasL[Range[20]],OddQ[Sqrt[1+8#]]&] (* Harvey P. Dale, Oct 18 2015 *)

PARI

L0=2; L1=1
{ for(k=1,10^9,
    if ( ispolygonal(L0,3), print1(L0,", ") );
    [L0, L1] = [L1, L1 + L0];
); }
\\ Joerg Arndt, Dec 06 2014