Quote from: tarrant_01 on January 06, 2016, 04:56:57 PM

I noticed that the results for x increase then reset every 3 steps, 0-2, 3-5, 6-8, etc...except for 15-21, this pattern continues when n > 21. Just a simple observation, hopefully helpful, probably not though.

Quote from: Bulista on January 06, 2016, 10:46:00 AM

Here are the results for the values we know given those 2 mentioned formulas:

y = 2^n * x

and so x = y / 2^n

AND

y = 2^n + x

and so x = y - 2^n

n	Known Results (y)	x = y / 2^n	x = y - 2^n
0	1	1.00000000	0
1	3	1.50000000	1
2	7	1.75000000	3
3	8	1.00000000	0
4	21	1.31250000	5
5	49	1.53125000	17
6	76	1.18750000	12
7	224	1.75000000	96
8	467	1.82421875	211
9	514	1.00390625	2
10	1155	1.12792969	131
11	2683	1.31005859	635
12	5216	1.27343750	1120
13	10544	1.28710938	2352
14	26867	1.63983154	10483
15	51510	1.57196045	18742
16	95823	1.46214294	30287
17	198669	1.51572418	67597
18	357535	1.36388779	95391
19	863317	1.64664650	339029
20	1811764	1.72783279	763188
21	3007503	1.43408918	910351
22	5598802	1.33485842	1404498
23	14428676	1.72003222	6040068
24	33185509	1.97801048	16408293
25	54538862	1.62538475	20984430
26	111949941	1.66818412	44841077
27	227634408	1.69600850	93416680
28	400708894	1.49275696	132273438
29	1033162084	1.92441434	496291172
30	2102388551	1.95800192	1028646727
31	3093472814	1.44051053	945989166
32	7137437912	1.66181426	2842470616
33	14133072157	1.64530614	5543137565
34	20112871792	1.17072322	2933002608
35	42387769980	1.23364647	8028031612
36	100251560595	1.45885221	31532083859
37	146971536592	1.06935867	9532583120
38	323724968937	1.17770458	48847061993
39	1003651412950	1.82563129	453895599062

Very interesting observation!!! Thank you for sharing