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
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
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