Old AI

On the Subject of Old AI

He hasn't forgotten his desire to escape.

When selected, Old AI will enter a trance-like state and display a series of numbers that all follow one condition.
A code must be typed in to prevent Old AI from completing integration; the code must follow the condition that is the reverse of the used condition. E.G. If the condition is Group 1, Subgroup 2, then the condition you must follow is Group 2, Subgroup 1.
In the event that both the Group and Subgroup match, the next matching Group/Subgroup pair must be submitted, wrapping around to the first. (I.E. Group 1, Subgroup 1; next would be Group 2, Subgroup 2) Under most conditions, the code must be 5-7 digits.

Group 1	Group 2
The sum of letters in each digit is a factor of the number. The number is a sequence that can be found within the first five hundred digits of Pi. The number is one less than a power of two. The number is two cubes concatenated. The number is divisible by seven.	The number is divisible by either two or three, but not six. The number contains a four in an odd position. 8. The number contains 108, with extraneous digits potentially lying in between 108. The number can be found within the first five hundred digits of e.
Group 3	Group 4
The number is a perfect square. The number, when converted to hexadecimal, contains D, E, A, or F. The sum of the digits is prime. The number has no repeating digits. The number has four consecutive ascending digits.	The number is prime. Each digit is either half (rounding down) or double the digit before it. The number has a leading zero. The number has either the month or year contained within it. The number contains a four digit number from 1234 to 4321.
Group 5
The number is at most five away from a perfect cube. The number is palidromic. Each digit is either greater than the one before it or is zero. The number is 9999999. The number modulo nine is not even.

Assisting Number References

First 500 significant digits of e:

27182818284590452353
60287471352662497757
24709369995957496696
76277240766303535475
94571382178525166427
42746639193200305992
18174135966290435729
00334295260595630738
13232862794349076323
38298807531952510190
11573834187930702154
08914993488416750924
47614606680822648001
68477411853742345442
43710753907774499206
95517027618386062613
31384583000752044933
82656029760673711320
07093287091274437470
47230696977209310141
69283681902551510865
74637721112523897844
25056953696770785449
96996794686445490598
79316368892300987931

First 500 significant digits of pi:

31415926535897932384
62643383279502884197
16939937510582097494
45923078164062862089
98628034825342117067
98214808651328230664
70938446095505822317
25359408128481117450
28410270193852110555
96446229489549303819
64428810975665933446
12847564823378678316
52712019091456485669
23460348610454326648
21339360726024914127
37245870066063155881
74881520920962829254
09171536436789259036
00113305305488204665
21384146951941511609
43305727036575959195
30921861173819326117
93105118548074462379
96274956735188575272
48912279381830119491

Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, ...

Perfect Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, ...

Perfect Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, ...

Assisting Number References (Continued)

Dec	Hex	Dec	Hex	Dec	Hex	Dec	Hex
0	0	4	4	8	8	12	C
1	1	5	5	9	9	13	D
2	2	6	6	10	A	14	E
3	3	7	7	11	B	15	F