Question

give the general term of the sequence 1,2,3,5,10,15,25,...

Type "integer sequences" in google:

Fibonacci numbers written in base 8:

1, 2, 3, 5, 10, 15, 25, 42, 67, 131, 220, 351, 571, 1142, 1733, 3075, 5030, 10125, 15155, 25302, 42457, 67761, 132440, 222421, 355061, 577502, 1154563, 1754265, 3131050, 5105335, 10236405, 15343742


When expressed in base 4, and then interpreted in base 9, is a multiple of the original number:

1, 2, 3, 5, 10, 15, 25, 75, 100, 125, 355, 435, 500, 1775, 2415, 3675, 5825, 9660, 14700, 17074, 20786, 22382, 23300, 27300, 79716, 83144, 87087, 97860, 103930, 125460, 172105, 331275, 332576, 348348, 415720, 1325100, 1330304, 1531980

The following number seems to be determined by the addition of the two previous numbers. I don't know about the connection with Fibonacci numbers.

I'm not sure about how to indicate it in general terms, but it might be something like the following:

Value (n - 2) + Value (n -1) = Value n

That isn't it, but it might help you think of the right notation. I hope it helps a little more. Thanks for asking.