Mathematical sequences challenge. Need your help.
I have these mathematical sequences that were given to me by my brother as a challenge. I believe they came from his daughter's homework, though we are not trying to help her cheat. He's just challenged me to solve them because he was unable. He wants to see how smart/resourceful I am. I'm allowed to use 'all the powers of the internet at my disposal' to try and solve these. (That's the resourceful part.) For me that includes you, I hope.
I think I may have the answers anyway, but I'd like your second opinion.
I've taken a picture of five of these sequences. The first two are simple and are solved. They are just there for example.
I believe that the soltion to the 3rd is:
1 , 1*2 , 1*2*3 , 24 , 1*2*3*4*5 , 1*2*3*4*5*6, 5040
The 4th and 5th I'm less confident about. I'm not sure what the subscripts mean. I guessed (perhaps incorrectly) that they represent a number system other than base 10. So base 5 and base 7. None of the numbers in the sequences so far violate those number systems. If that assumption is correct, I came up with the following:
1, 4, 12, 22, 23, 31 (with the little 5 subscripts)
1, 4, 12, 22, 34, 51, 100 (with the 7s)
I'm quite ready to believe that I'm wrong.
What do you think? Am I right? If not, what is?