@gteeyore,
I have not posted for many many months, I am usually at work or have nothing to add, however, I think for a change I may be of some help.
Write out the digits of pi to many many decimal places.
1st digit is the 1st number in the sequence.
Add the next 2 digits of pi = 2nd number in the sequence.
Add the next 3 digits of pi = 3rd number in the sequence.
And so on.
Apologies to those that will be annoyed for the spoiler.