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A248506 Lucas numbers that are also triangular numbers. 2
1, 3, 5778 (list; graph; refs; listen; history; text; internal format)
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: A307210 A171362 A249511 * A034317 A185671 A338412

Adjacent sequences:  A248503 A248504 A248505 * A248507 A248508 A248509

KEYWORD

nonn,fini,full,bref

AUTHOR

Vincenzo Librandi, Dec 06 2014

STATUS

approved

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Last modified July 27 07:50 EDT 2021. Contains 346304 sequences. (Running on oeis4.)