Following up on this question,

http://math.stackexchange.com/questions/1788015/is-112122132142152162-1111-special/1788102?noredirect=1#comment3649733_1788102

is anything known about the sequence of those repdigits (i.e. $1111, 44444$), which are expressible as the sum of squares of consecutive numbers?

In particular, are there infinitely many of them?

Edit: The question is not restricted to base $10$, but this is the case I am most interested in. A heuristic argument (see above link) suggests that there may be only finitely many after all. For all I know so far, this may or may not depend on the base.

Following up on this question,

https://math.stackexchange.com/questions/1788015/is-112122132142152162-1111-special/1788102?noredirect=1#comment3649733_1788102

is anything known about the sequence of those repdigits (i.e. $1111, 44444$), which are expressible as the sum of squares of consecutive numbers?

In particular, are there infinitely many of them?

Edit: The question is not restricted to base $10$, but this is the case I am most interested in. A heuristic argument (see above link) suggests that there may be only finitely many after all. For all I know so far, this may or may not depend on the base.

Following up on this question,

http://math.stackexchange.com/questions/1788015/is-112122132142152162-1111-special/1788102?noredirect=1#comment3649733_1788102

is anything known about the sequence of those repdigits (i.e. $1111, 44444$), which are expressible as the sum of squares of consecutive numbers?

In particular, are there infinitely many of them?

Edit: The question is not restricted to base $10$, but this is the case I am most interested in. A heuristic argument in the above link suggests that there may be only finitely many after all (this may or may not depend on the base for all I know so far).

Following up on this question,

http://math.stackexchange.com/questions/1788015/is-112122132142152162-1111-special/1788102?noredirect=1#comment3649733_1788102

is anything known about the sequence of those repdigits (i.e. $1111, 44444$), which are expressible as the sum of squares of consecutive numbers?

In particular, are there infinitely many of them?

Edit: The question is not restricted to base $10$, but this is the case I am most interested in. A heuristic argument (see above link) suggests that there may be only finitely many after all. For all I know so far, this may or may not depend on the base.