What comes next?

[Thomas Klemm]

This program might be faster:

Code:

\<< DUP ROT + SWAP DUP { } + SWAP ROT
  \<< - ROT OVER + SWAP ROT OVER + SWAP
  \>> STREAM DROP
\>>

It is of order \(\mathcal{O}(n)\) instead of \(\mathcal{O}(n^2)\) and works similarly to my initial program for the HP-42S.

Example

{ 1 }
2
NXT

{ 2 1 }
3

DROP 4
NXT

{ 4 2 1 }
7

DROP 8
NXT

{ 8 4 2 1 }
15

DROP 16
NXT

{ 16 8 4 2 1 }
31

NXT

{ 31 15 7 3 1 0 }
57

NXT

{ 57 26 11 4 1 0 0 }
99

NXT

{ 99 42 16 5 1 0 0 0 }
163

NXT

{ 163 64 22 6 1 0 0 0 0 }
256