A180928 1 + product of any two terms is a triangular number.

0, 1, 5, 27

Offset

1,3

Comments

The sequence could also start 0, 1, 2, 27, ... - R. J. Mathar, Oct 03 2010

This sequence is also finite and complete. - Max Alekseyev, Feb 16 2011

If 1*x+1, 5*x+1, 27*x+1 are triangular numbers, then 8*x+9=p^2, 40*x+9=q^2, 216*x+9=r^2 for some integers p,q,r. They should also satisfy the system of equations { 5*p^2 - q^2 = 36, 27*p^2 - r^2 = 234 } which has no integer solutions. See Alekseyev, 2011.

A192225 contains another result from the same paper.

Links

Table of n, a(n) for n=1..4.

Max A. Alekseyev (2011). On the Intersections of Fibonacci, Pell, and Lucas Numbers, INTEGERS 11(3), pp. 239-259. doi:10.1515/INTEG.2011.021

Example

(0*1)+1 = 1 is triangular.
(0*5)+1 = 1 is triangular.
(1*5)+1 = 6 is triangular.
(0*27)+1 = 1 is triangular.
(1*27)+1 = 28 is triangular.
(5*27)+1 = 136 is triangular.
(0*70)+1 = 1 is triangular.
(1*70)+1 = 71 is NOT triangular, so 70 is not the next value.
(5*70)+1 = 351 is triangular.
(27*70)+1 = 1891 is triangular.

Crossrefs

This is to A030063 as A000217 is to A000290.

Sequence in context: A281747 A064489 A081089 * A366332 A342998 A342997

Adjacent sequences: A180925 A180926 A180927 * A180929 A180930 A180931

Keyword

nonn,full,fini

Author

Jonathan Vos Post, Sep 25 2010

Extensions

No further terms below 10^20. - Charles R Greathouse IV, Sep 29 2010

Keywords 'full', 'fini' from Max Alekseyev, Feb 16 2011

Status

approved