18:15 Friday 25 August 2017 JST
Messing around with Collatz Conjecture, I came across a river of zeros in the result of this one. Is that common?
91: 167172348149023738268218170602359284156167596286878693384519680000018347272
92: 83586174074511869134109085301179642078083798143439346692259840000009173636
93: 41793087037255934567054542650589821039041899071719673346129920000004586818
94: 20896543518627967283527271325294910519520949535859836673064960000002293409
95: 62689630555883901850581813975884731558562848607579510019194880000006880228
96: 31344815277941950925290906987942365779281424303789755009597440000003440114
97: 15672407638970975462645453493971182889640712151894877504798720000001720057
98: 47017222916912926387936360481913548668922136455684632514396160000005160172
99: 23508611458456463193968180240956774334461068227842316257198080000002580086
100: 11754305729228231596984090120478387167230534113921158128599040000001290043
101: 35262917187684694790952270361435161501691602341763474385797120000003870130
102: 17631458593842347395476135180717580750845801170881737192898560000001935065
103: 52894375781527042186428405542152742252537403512645211578695680000005805196
104: 26447187890763521093214202771076371126268701756322605789347840000002902598
105: 13223593945381760546607101385538185563134350878161302894673920000001451299
106: 39670781836145281639821304156614556689403052634483908684021760000004353898
107: 19835390918072640819910652078307278344701526317241954342010880000002176949
108: 59506172754217922459731956234921835034104578951725863026032640000006530848
109: 29753086377108961229865978117460917517052289475862931513016320000003265424
110: 14876543188554480614932989058730458758526144737931465756508160000001632712
I found it after starting with 2^222 from https://www.tsm-resources.com/alists/pow2.html
https://www.nitrxgen.net/collatz/6739986666787659948666753771754907668409286105635143120275902562304
and I tacked on some random mostly-odd numbers, 7397177935881, to see what would happen.
So let’s see what happens when I tack the same numbers on the end of the 2^221
Well! There they are again..
Okay, how about tacking the same postfix on 2^159.
https://www.nitrxgen.net/collatz/7307508186654514591018424163581415098279662714887397177935881
And they they are again.
Okay okay so lemme take all these and mess with the postfix to see if the rivers of zeros stay intact.
- https://www.nitrxgen.net/collatz/67399866667876599486667537717549076684092861056351431202759025623047397777777777/
- https://www.nitrxgen.net/collatz/3369993333393829974333376885877453834204643052817571560137951281152739777777777/
- https://www.nitrxgen.net/collatz/73075081866545145910184241635814150982796627148873977777777/
They do!
Okay, so it must be basically that the power of two prefix is shrinking as planned and leaving some stuff on the right which slowly takes care of itself via the Collatz equation.
oooohh so if that is the case, we should get two rivers of zeros if we start with two power of two numbers and then extra bits on the end.
2^75 = 37778931862957161709568
here it is twice
3777893186295716170956837778931862957161709568
Then tack on some numbers at the end
https://www.nitrxgen.net/collatz/377789318629571617095683777893186295716170956877777777777777777/
37: 769482217582755840000007694822175827558400000158417969944
38: 384741108791377920000003847411087913779200000079208984972
39: 192370554395688960000001923705543956889600000039604492486
40: 96185277197844480000000961852771978444800000019802246243
41: 288555831593533440000002885558315935334400000059406738730
42: 144277915796766720000001442779157967667200000029703369365
43: 432833747390300160000004328337473903001600000089110108096
44: 216416873695150080000002164168736951500800000044555054048
45: 108208436847575040000001082084368475750400000022277527024
46: 54104218423787520000000541042184237875200000011138763512
47: 27052109211893760000000270521092118937600000005569381756
48: 13526054605946880000000135260546059468800000002784690878
49: 6763027302973440000000067630273029734400000001392345439
50: 20289081908920320000000202890819089203200000004177036318
51: 10144540954460160000000101445409544601600000002088518159
52: 30433622863380480000000304336228633804800000006265554478
53: 15216811431690240000000152168114316902400000003132777239
54: 45650434295070720000000456504342950707200000009398331718
55: 22825217147535360000000228252171475353600000004699165859
56: 68475651442606080000000684756514426060800000014097497578
57: 34237825721303040000000342378257213030400000007048748789
58: 102713477163909120000001027134771639091200000021146246368
Bingo. Okay that’s enough.