thecages

wrote an ugly perl script to brute force a^(a+1) = (a+1)^a
at the moment it uses normal floats and I think that is what is limiting it to 48 digits.
next I want to extend it to use Math::BigFloat and see if I can get further.

here's the output:

Let's brute a^(a+1) = (a+1)^a
Using Floater

It's somewhere between 2 and 3...
1 a= 2.5000000000000000000000000000000000000000000000000000000000000000
2 a= 2.2500000000000000000000000000000000000000000000000000000000000000
3 a= 2.3750000000000000000000000000000000000000000000000000000000000000
4 a= 2.3125000000000000000000000000000000000000000000000000000000000000
5 a= 2.2812500000000000000000000000000000000000000000000000000000000000
6 a= 2.2968750000000000000000000000000000000000000000000000000000000000
7 a= 2.2890625000000000000000000000000000000000000000000000000000000000
8 a= 2.2929687500000000000000000000000000000000000000000000000000000000
9 a= 2.2949218750000000000000000000000000000000000000000000000000000000
10 a= 2.2939453125000000000000000000000000000000000000000000000000000000
11 a= 2.2934570312500000000000000000000000000000000000000000000000000000
12 a= 2.2932128906250000000000000000000000000000000000000000000000000000
13 a= 2.2930908203125000000000000000000000000000000000000000000000000000
14 a= 2.2931518554687500000000000000000000000000000000000000000000000000
15 a= 2.2931823730468750000000000000000000000000000000000000000000000000
16 a= 2.2931671142578125000000000000000000000000000000000000000000000000
17 a= 2.2931594848632812500000000000000000000000000000000000000000000000
18 a= 2.2931632995605468750000000000000000000000000000000000000000000000
19 a= 2.2931652069091796875000000000000000000000000000000000000000000000
20 a= 2.2931661605834960937500000000000000000000000000000000000000000000
21 a= 2.2931666374206542968750000000000000000000000000000000000000000000
22 a= 2.2931663990020751953125000000000000000000000000000000000000000000
23 a= 2.2931662797927856445312500000000000000000000000000000000000000000
24 a= 2.2931663393974304199218750000000000000000000000000000000000000000
25 a= 2.2931663095951080322265625000000000000000000000000000000000000000
26 a= 2.2931662946939468383789062500000000000000000000000000000000000000
27 a= 2.2931662872433662414550781250000000000000000000000000000000000000
28 a= 2.2931662909686565399169921875000000000000000000000000000000000000
29 a= 2.2931662891060113906860351562500000000000000000000000000000000000
30 a= 2.2931662881746888160705566406250000000000000000000000000000000000
31 a= 2.2931662877090275287628173828125000000000000000000000000000000000
32 a= 2.2931662874761968851089477539062500000000000000000000000000000000
33 a= 2.2931662873597815632820129394531250000000000000000000000000000000
34 a= 2.2931662874179892241954803466796875000000000000000000000000000000
35 a= 2.2931662873888853937387466430664062500000000000000000000000000000
36 a= 2.2931662874034373089671134948730468750000000000000000000000000000
37 a= 2.2931662874107132665812969207763671875000000000000000000000000000
38 a= 2.2931662874143512453883886337280273437500000000000000000000000000
39 a= 2.2931662874125322559848427772521972656250000000000000000000000000
40 a= 2.2931662874116227612830698490142822265625000000000000000000000000
41 a= 2.2931662874120775086339563131332397460937500000000000000000000000
42 a= 2.2931662874118501349585130810737609863281250000000000000000000000
43 a= 2.2931662874119638217962346971035003662109375000000000000000000000
44 a= 2.2931662874119069783773738890886306762695312500000000000000000000
45 a= 2.2931662874118785566679434850811958312988281250000000000000000000
46 a= 2.2931662874118643458132282830774784088134765625000000000000000000
47 a= 2.2931662874118572403858706820756196975708007812500000000000000000
48 a= 2.2931662874118607930995494825765490531921386718750000000000000000
49 a= 2.2931662874118625694563888828270137310028076171875000000000000000
50 a= 2.2931662874118616812779691827017813920974731445312500000000000000
51 a= 2.2931662874118612371887593326391652226448059082031250000000000000
52 a= 2.2931662874118607930995494825765490531921386718750000000000000000
I'm stuck!
low  : 2.2931662874118607930995494825765490531921386718750000000000000000
high : 2.2931662874118612371887593326391652226448059082031250000000000000
diff : 0.0000000000000004440892098500626161694526672363281250000000000000

left : 15.3806325543004884792708253371529281139373779296875000000000000000
right: 15.3806325543004902556276647374033927917480468750000000000000000000
diff : -0.0000000000000017763568394002504646778106689453125000000000000000