This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A248506 #42 Jul 05 2025 09:58:46
%S A248506 1,3,5778
%N A248506 Lucas numbers that are also triangular numbers.
%C A248506 Intersection of A000032 and A000217.
%C A248506 All terms are shown, see Theorem 1.1 in the Tengely reference. - _Joerg Arndt_, Dec 06 2014
%D A248506 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 28.
%H A248506 Luo Ming, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/27-2/ming.pdf">On Triangular Fibonacci Numbers</a>, The Fibonacci Quarterly, 27.2 (1989), pp. 98-108.
%H A248506 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 A248506 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 A248506 Lucas(18) = 5778 = 107*108/2.
%t A248506 Select[LucasL[Range[20]],OddQ[Sqrt[1+8#]]&] (* _Harvey P. Dale_, Oct 18 2015 *)
%o A248506 (PARI)
%o A248506 L0=2; L1=1
%o A248506 { for(k=1,10^9,
%o A248506 if ( ispolygonal(L0,3), print1(L0,", ") );
%o A248506 [L0, L1] = [L1, L1 + L0];
%o A248506 ); }
%o A248506 \\ _Joerg Arndt_, Dec 06 2014
%Y A248506 Cf. A000032, A000217, A039595.
%K A248506 nonn,fini,full,bref
%O A248506 1,2
%A A248506 _Vincenzo Librandi_, Dec 06 2014