A248506
Lucas numbers that are also triangular numbers.
Original entry on oeis.org
Lucas(18) = 5778 = 107*108/2.
- James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 28.
- 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).
-
Select[LucasL[Range[20]],OddQ[Sqrt[1+8#]]&] (* Harvey P. Dale, Oct 18 2015 *)
-
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
A292851
Fibonacci numbers that are also generalized octagonal numbers.
Original entry on oeis.org
0, 1, 5, 8, 21, 4181
Offset: 0
Cf.
A039595 (triangular Fibonacci numbers).
A293023
Generalized pentagonal numbers that are also Pell numbers.
Original entry on oeis.org
0, 1, 2, 5, 12, 70
Offset: 0
- V. Sima Rama Prasad and B. Srinivasa Rao, Pentagonal Numbers in the Pell Sequence and Diophantine Equations 2x^2=y^2(3y-1)^2+-2, The Fibonacci Quarterly, Vol. 40, No. 3 (2002), 233-241.
- Szabolcs Tengely, Finding g-gonal numbers in recurrence sequences, Fibonacci Quarterly, vol.46/47, No. 3 (2009), 235-240.
A294369
Indices of Fibonacci numbers (A000045) that are triangular numbers (A000217).
Original entry on oeis.org
0, 1, 2, 4, 8, 10
Offset: 1
Fibonacci(10)=55 is a triangular number, therefore 10 is in the sequence.
A307991
Fibonacci numbers of the form k^2 - k - 1 with integer k.
Original entry on oeis.org
89 is in the sequence since 89 = 10^2 - 10 - 1 or equivalently 1/89 = 1/10^2 + 1/10^3 + 2/10^4 + 3/10^5 + 5/10^6 + ... This is why the first digits of the decimal expansion of 1/89 = 0.011235... are the first terms of the Fibonacci sequence.
- Fenton Stancliff, A curious property of a_11, Scripta Math., Vol. 19 (1953), p. 126.
Showing 1-5 of 5 results.
Comments