0,1,2,4,8,16,32,64,128,256,512,?
wolframalpha.com
wolframalpha.com
0,1,2,4,8,16,32,64,128,256
and
0,1,2,4,8,16,32,64,128,256,512,1024
come back accurately.
Because you need to beat Alpha over the head with data in order to convince it to say "well, maybe the first value just doesn't fit the pattern".
As a mathematician, I'd say that Alpha's approach here is entirely reasonable.
0,1,2,4,8,16,32,64,128,256
it detects the pattern, but if you tack on the 512 it duffs it.
R code:
solver <- function(x) {
print(x)
if (length(x) == 0 || all(x == 0))
0
else
x[length(x)] + solver(diff(x))
}
solver(c(0,1,2,4,8,16,32,64,128)) #=> 255
solver(c(0,1,2,4,8,16,32,64,128,256)) #=> 512
solver(c(0,1,2,4,8,16,32,64,128,256,512)) #=> 1023
solver(c(0,1,2,4,8,16,32,64,128,26,512,1024)) #=> 2048