Next number: 61, 115, 771, 4129, 15649, ?

[daskalou]

Find the next number in the sequence:

61, 115, 771, 4129, 15649

 

[Borek]

Apart from the obvious answer of 11111...

Spoiler

46671

 

[daskalou]

The man with the green hair is correct. Well done Borek! :)

How did you figure it out?

 

[Borek]

Intuition and trial and error. I started comparing original sequence with others - like n^x and xⁿ, observing the difference - too much here, not enough here, too fast, too slow, guessing what kind of function differences are and creating new sequences from those powers and those functions... and at some point differences between my sequence and original sequence were in arithmetic progression. Ability to do menthal arithmetic helped at this point enormously although most of the trial and error was done with spreadsheet. Somewhere between 5 and 10 minutes.