[math-fun] new inverter, new format : 2.459 billion mathematical constants.
Hello, I am downloading it now, the new version of my inverter. I changed the format to 64 digits and normalized. Well, there are 2.459 billion mathematical constants in it. This time I used Maple and Mathematica and in some occasion Pari-Gp to generate the numbers. The data is presently <dumped> into a work directory here : http://www.lacim.uqam.ca/~plouffe/ip/ the files are gziped, to take a look at one just click on the file and normaly the firefox browser will uncompress it on the fly. If you do not use firefox you may save it on your computer and uncompress it with winrar of gunzip (unix). The pc (actualy it is a mac) where the database will reside is currently being organized in Montréal, there are 90000 files for a total of 297 gigabytes. The disk is a 300 gigabytes, so I think it is time I stop generating constants! In the database there are something like 25 million constants that were generated by the OEIS database. For the moment, I intend to at least organize the data so that anybody interested in it may download (yes download) the database. This summer I intend to re-work the lookup script to take into account that new format. The database it of course what I think is an interesting constant. The base table has about 186 known constants http://www.lacim.uqam.ca/~plouffe/b000.txt and the rest are entries similar to the first and second versions of this project (the inverse symbolic calculator 1995-now) the plouffe inverter (1998-now). If you have any suggestions, of course they are welcome. note : the current plouffe_inverter program to analyze math constants will be compatible with the new format of course. It is still in Maple syntax, I should change it to mathematica, mathematica is faster, much faster than maple for many computations... For the nostalgic, the current inverter with 200 million constants is all here : http://www.lacim.uqam.ca/~plouffe/plouffe_inverter_tables/ Simon Plouffe
Hello Math-Fun, We are looking for an 18-digit integer (like 946131483695200285) where we have "d" digits between two d's (here: one digit between two 1's, zero digit between the two 0's, nine digits between the two 9's, etc.) Those 18 digits form thus 9 pairs of digits -- the 9 pairs being different one from another. Now cut this integer in chunks so to make a finite monotonically increasing sequence (like this one, for instance, among others): 9,46,131,483,695,200285 We sum the terms: 9+46+131+483+695+200285 = 201649 Question: Find the integer which, properly chunked, will give the smallest possible sum. --- Example #2: 849362432856900151 could give: 8+49+362+432+856+900151 = 901858 ... but if we move the first digit "8" to the end (which is still sound), 849362432856900151 becomes 493624328569001518 ... which, properly chunked, will give: 4+9+362+432+856+900+1518 = 4080 This is my personal best so far. Regards, E. --- P.S. a 20-digit integer such as described is impossible for parity reasons. I'll be delighted to receive the full b-file list of all such 18-digit integers (if someone would be kind enough to compute it).
participants (2)
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Eric Angelini -
Simon Plouffe