Saturday 2 January 2010

A Palindromic Date, and A Problem

01/02/2010.... or 01022010 Ok, technically that is not a Palindrome, or else numbers like 110 would be palindromes. But still,close enough to be special as pointed out by my lovely sweetheart.

How unusual is that??? Well, there are only 19,998 numbers less than 100,000,000 that are palindromes...I just came across this at the Wolfram Mathworld page.. The sum of the reciprocals of the palindromic numbers ( 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212...) converges to a constant...... approx 3.37018..
Strange, but as numbers get bigger, prime palindromes get very rare it seems...2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 10301, 10501, 10601, 11311, 11411, 12421, 12721, 12821, 13331, 13831, 13931, 14341, and it seems that after eleven, there are no palindromic primes that have an even number of digits (Every palindrome with an even number of digits is divisible by 11).

Next year on Nov 20, we get a real palindromic date, 11/02/2011.... Now that IS unusual.. Ok, and the next one after that is?????

Addendum, Professor Charles Wells of Case Western Reserve suggested a follow up, "Count the number of dates in the American system that are palindromes by something cleverer than brute force. " Well, I didn't actually do that, but I did take a moment to figure out that, if my math doodles are right, there was not such an event from 12/31/1321 (oops, think that should be 09/31/1390... "mia culpa") until 10/02/2001... then after the Jan 2nd this year, and Nov of next year... (and the one you have to figure out that comes after that)... well, there just are not very many of them...

also... I just read somewhere that we who are alive today (those of us over 20) are kind of blessed because we have lived through two palindromic years... 1991 and 2002, and that won't happen to anyone again for about a thousand years unless someone does discover a way not to die in anything like what we consider a normal lifetime now-a-days... lucky me.. lucky you???


Charles Wells said...

This raises the questions: (1) Count the number of dates in the American system that are palindromes by something cleverer than brute force. (2) Ditto for the number of dates in the European system

Pat's Blog said...

Charles, good idea...see addendum to post, and thanks