How can this sequence be continued, 1, 3, 7, 15, 31…?

The sequence pattern is: (2^n)-1 Therefore, (2^1)-1 = 1 (2^2)-1 = 3 (2^3)-1 = 7 (2^4) -1 = 15 (2^5) -1 = 31 and (2^6) -1 = 63 Similarly, (2^7) -1 = 127 So, the next term in the sequence 1, 3, 7, 15, 31 ... Then we can notice that the sequence can be generated by this “rule”: [math]a_0 = 1, a_{n+1} = 2*a_n+1, \forall n \in \N[/math]. read more

[math]1, 3, 7, 15, 31 \tag{1}[/math] into The On-Line Encyclopedia of Integer Sequences® (OEIS®) returned [math]81[/math] results circa July 20-th 2017 - that is [math]81[/math] distinct sequences with the same pattern of initial terms as (1). read more