A248506 - OEIS

%I #36 Oct 18 2015 14:05:55

%S 1,3,5778

%N Lucas numbers that are also triangular numbers.

%C Intersection of A000032 and A000217.

%C All terms are shown, see Theorem 1.1 in the Tengely reference. - _Joerg Arndt_, Dec 06 2014

%H Luo Ming, <a href="http://www.fq.math.ca/Scanned/27-2/ming.pdf">On Triangular Fibonacci Numbers</a>, The Fibonacci Quarterly, 27.2 (1989), pp. 98-108.

%H Luo Ming, <a href="http://dx.doi.org/10.1007/978-94-011-3586-3_26">On Triangular Lucas Numbers</a>, Applications of Fibonacci Numbers, 1991, pp 231-240.

%H Szabolcs Tengely, <a href="http://www.math.unideb.hu/~tengely/G-gonal.pdf">Finding g-gonal numbers in recurrence sequences</a>, Fibonacci Quarterly, vol.46/47, no.3, pp.235-240, (2009).

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

%t Select[LucasL[Range[20]],OddQ[Sqrt[1+8#]]&] (* _Harvey P. Dale_, Oct 18 2015 *)

%o (PARI)

%o L0=2; L1=1

%o { for(k=1,10^9,

%o     if ( ispolygonal(L0,3), print1(L0,", ") );

%o     [L0, L1] = [L1, L1 + L0];

%o ); }

%o \\ _Joerg Arndt_, Dec 06 2014

%Y Cf. A000032, A000217, A039595.

%K nonn,fini,full,bref

%O 1,2

%A _Vincenzo Librandi_, Dec 06 2014