
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.


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.
