Largest Number in Brainfuck BigInt for each program length up to 50 instructions This challenge is for the largest finite number you can get BrainFuck programs of given lengths to contain in memory.

We must use one of the BF versions that uses big integers for the cells rather than byte values as not to be capped at 255. Do not use negative positions and values in memory. Do not use the BF instruction to input memory, also the output instruction is not needed.



Challenge:

Write Brainfuck programs with lengths from 0 to 50. Your score is the sum of each programs maximum value in memory.



As they may well be trivial feel free to omit the programs listed below and start from a length of 21, I'll use the following for the smaller sizes:

Length, Score, Program

0, 0
1, 1, +
2, 2, ++
3, 3, +++
Pattern Continues
10, 10, ++++++++++
11, 11, +++++++++++
12, 12, ++++++++++++
13, 16, ++++[-&gt;++++&lt;]
14, 20, +++++[-&gt;++++&lt;]
15, 25, +++++[-&gt;+++++&lt;]
16, 30, ++++++[-&gt;+++++&lt;]
17, 36, ++++++[-&gt;++++++&lt;]
18, 42, +++++++[-&gt;++++++&lt;]
19, 49, +++++++[-&gt;+++++++&lt;]
20, 56, ++++++++[-&gt;+++++++&lt;]


Total Score: 352



Related but different:

Large Numbers in BF

Largest Number Printable

Busy Brain Beaver

See the comments below for more info.





The combined results so far, being the sum of the best of each size:

length: 50
by l4m2


(262) - 2



length: 49
by l4m2


(212) - 2



length: 48
based on code by l4m2, by alan2here


(172) - 2



length: 39 to 47
based on code by l4m2, by alan2here


Σ (n = 4 to 12) of (fn(0) | f(x) := (4x+2 - 4) / 3)



length: 38
based on code by l4m2, by alan2here


(4^1366 - 4) / 3



length: up to 37
by alan2here

x |
  x &gt; 6 ^ 20
  x &gt; n
  x ≈ n
  n = 3,657,880,038,459,860
(262)-2

+++++[-&gt;+++++&lt;]&gt;[-&gt;+[-&gt;+[-&gt;++&lt;]&gt;[-&lt;+&gt;]&lt;&lt;]&lt;[-&gt;+&lt;]&gt;]


Where (42) = 2222

f20(0), where f(x):=(4x+2-4)/3

++++[-&gt;+++++&lt;]&gt;[-&gt;+[-&gt;+[-&gt;++&lt;]&gt;[-&lt;++&gt;]&lt;&lt;]&lt;[-&gt;+&lt;]&gt;]