A248506 Lucas numbers that are also triangular numbers.

1, 3, 5778

Offset

1,2

Comments

Intersection of A000032 and A000217.

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

Links

Table of n, a(n) for n=1..3.

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).

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000032, A000217, A039595.

Sequence in context: A171362 A249511 A362099 * A368622 A034317 A185671

Adjacent sequences: A248503 A248504 A248505 * A248507 A248508 A248509

Keyword

nonn,fini,full,bref

Author

Vincenzo Librandi, Dec 06 2014

Status

approved