Suppose I have a sequence generated by a polynomial, and the first three terms are 1,2,3. What is the set of polynomials that could have been used to generate this sequence? Is it the same as the set which would generate 1,2,3,4?

Let's see:
0-(-8)= 8 #8
8-0=8 #8
61-8=53 & 5+3=8 #8
96-61=35 & 3+5=8 #8
401-96=305 & 3+0+5=8 #8
904-401=503 & 5+0+3=8 #8
If my logic is correct the next sum should be a 4 digit number either 3005 or 5003 so it should be either 3909 or 5907. My guess is 5907.

Originally posted by royalchicken I was just thinking ''add 8 and reverse the digits'', so: -8, 0, 8, 61, 96, 401, 904, 219, 722, 37, ....

Acolyte, I'll try to answer you question in a bit.

That's pretty cool. I did it the same way as Richard Parker. I didn't even see it the way Royalchicken did it until I saw his explination.

DragonKnights, which was the solution you were looking for? Obviously they are both correct given their explanations, but which follows your original pattern?

Originally posted by econundrum I believe the next term in the sequence is 1.

You are correct. I think I may have included too many terms. This one was a lateral sequence: it is the number of bongs on a standard grandfatcher clock. ðŸ˜›