Zorac (zorac) wrote,
Zorac
zorac

Playing with numbers...

I was idly playing with numbers in my head the other day, something to occupy my mind while I trudged back from Sainsbury's with a load of shopping. In particular, I was looking at number sequences (you know, what number comes next - 1, 3, 5, 7, ? or 1, 4, 9, 16, ?) and came up with the following (related, but calculated in opposite ways):

1 ... 4 ... 19,683 ... ?
1 ... 4 ... 7,625,597,484,987 ... ?

The answer to the first series is a mere
340,282,366,920,938,463,463,374,607,431,768,211,456
The second, as you can probably guess, is larger. Much larger. In fact, it's exactly
226,815,615,859,885,194,199,148,049,996,411,692,254,958,731,641,184,786,755,447,122,887,443,528,060,147,093,953,603,748,596,333,806,855,380,063,716,372,972,101,707,507,765,623,893,139,892,867,298,012,168,192
or approximately
5 x 108,072,304,726,028,225,379,282,369,632,412,842,737,810,037,345,818,396,835,407,833,195,922,269,447,488,939,454,873,506,883,657,604,175,736,107,203,603,983,535,115,431,016,379,958,411,831,793,261,615,652,260
Even more approximately, that's
5 x 108 x 10153
Time to play with some big numbers:
5 x 10googol x 8 x 1053
5 x googolplex8,000 x 1050
5 x googolplex8,000 √googol

However I put it, that is one very big number, almost impossible to visualise - Asimov's essay Skewered! details just how hard to visualise big numbers can be. Final challenge, if you want to prove that you actually solved the puzzle: explain how the series was derived.
Tags: geekery
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  • 19 comments

jiggery_pokery

September 5 2003, 13:44:26 UTC 17 years ago

I'm guessing at - let's see if HTML is good enough to be able to produce this -

1 , 22, 333, 4444

and a similar thing for the second one but instead of there being n recursions of "powers of n", there are n! recursions of "powers of n".

Yay HTML! :-)

zorac

September 5 2003, 14:00:11 UTC 17 years ago

And in a mere 6 minutes from my original posting ;-)
Actually, they're poth the series you gave, just calculated in oposite directions, the first being
1, 22, (33)3, ((44)4)4
and the second
1, 22, 3(33), 4(4(44))

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