That sequence in particular traverses the array produced by looking at Abulsme(L,S) for all valid combinations of L and S starting with Abulsme(1,1); Abulsme(2,1); Abulsme(2,2); Abulsme(3,1); Abulsme(3,2); Abulsme(3,3); Abulsme(4,1); Abulsme(4,2); Abulsme(4,3); Abulsme(4,4); Abulsme(5,1); etc… In this way you get one infinite sequence with all values of the function.
Some other infinite sequences generated from the function by fixing S and increasing L (starting with L=S) have also been included.
The cases for S=1 and S=2 matched sequences already in the OEIS:
Only these have been added, although of course sequences can be generated with any positive integer S. These sequences do reach a limit with increasing S though, and the limit of the sequence has been added to the OEIS as well.
Woo! My mathematical masterpiece first documented when I was in 8th grade, and further expounded on from then until around my Freshman year of college, and basically untouched since then… which would be about 17 or 18 years now… is finally recognized. :-)
A certain person with the initials JPS once suggested that the Abulsme Function, when combined with 12 dimensional contour integration, could be used to go back and time and prevent the Space Shuttle Challenger from exploding.
Um… no.
But it is in the OEIS now.
Which is great.
Oh, and I should add, you can even listen to the sequence. I particularly like it when played by a marimba. It has now been added to my iTunes library. :-)
There are now two different types of ads on here rather than just the one that was there before. Neither will make me any cash of course, it is just a matter of trying out new things and seeing what they do. (I added ads to this site for the first time a few weeks short of a year ago, and I have yet to make my first $20, although I’m close!)
You’ll randomly get one type or another on each page view. Woo.
The dog left on the doorstep of the southern California pet clinic was sick. The letter left with him was heartbreaking.
“Dear Drs., please forgive me for this horrible transgression. I have no where else to turn so I ask you to mercifully, gently and lovingly please help him sleep. His name is Kaiser and he’s 16-and-a half years old. He’s been my friend, my teacher, my pupil, my lifelong loving and loyal companion,” the letter said.
On the envelope, the author of the letter said that he thought Kaiser had two strokes the night before.
“Be good to him as you would your own child, for he’s been mine for a loving lifetime,” the envelope read.
…
“I’m a homeless disabled vet, and I know when it’s time to say goodbye to a friend, and it’s time now. He’s such a part of my being, I’ll once again be alone in my life. I love you Kaiser, thank you for caring, sincerely, Kaiser’s Soul Mate.”
Debbie Herot, a manager at Pet Medical Center Chatoak in Granada Hills, found the letter and the dog on the clinic doorstep as she came in to work last week.
Though she tries to keep an emotional distance from the pets she sees, in this case, she couldn’t do it.
“After you’re in this business for so long you learn to look the other way, because we have to euthanize animals. This one i couldn’t euthanize,” Herot said.
A good article followed by good discussion on one of the topics I find fascinating… the theoretical right (or absence there of) of states to leave the United States. For the record, I was quite convinced by Jefferson Davis’ arguments in his memoirs that despite the loss in the war, and subsequent post-war SCOTUS opinions, the South probably SHOULD have been able to leave peacefully.
Now, the question of if the South’s reasons for leaving were legitimate, or if it would have been proper for the North to let them leave, recognize their independence as a separate and sovereign country, but then immediately declare war on the new country for purposes of making it submit and ending slavery and perhaps reincorporating it later… that’s a completely different question. That’s probably the way I think it should have played out. But that isn’t what happened, so it is a sort of moot point.
Anyway, good discussion in the article (and attached comments) for those interested:
I don’t think that belief in a right of secession by itself demonstrates ignorance about either law or American history. The Constitution is famously silent on the issue of secession. It doesn’t explicitly guarantee states a right to secede, but also doesn’t explicitly forbid secession. Interestingly, the Articles of Confederation explicitly stated that the union is “perpetual” (which seems to foreclose secession), but the Constitution which superseded the Articles does not include any such language. This silence has led to ongoing debate over the constitutional status of secession. Prior to the Civil War, many respected scholars and political leaders claimed that secession was permitted by the Constitution. Many were apologists for slavery, but by no means all. For example, political leaders from several northern free states asserted that they had a right to secede at the 1814 Hartford Convention. In light of this history and the ambiguity of the constitutional text, I don’t think that belief in a right to secession is at all unreasonable, much less a sign of obvious ignorance or stupidity.
Well, since I couldn’t sleep, and eventually got tired of Wikipedia and random shows on the Tivo, I ended up retrofitting my Random Spot Tool to get rid of the ancient and unfriendly MapQuest hack and replace it with an integrated Google Maps version using their Maps API.
At the same time, since now I could, I added a few things that were not possible the old way. It is much better and much more fun than before. Play with it and enjoy.
And maybe go on some trips!
Of course, now I haven’t slept at all. I took Amy to school, and am now going to have to rush through the rest of my morning activities to try to get to work at a semi-reasonable hour.
Out of all the US Presidential elections in the last 100 years (meaning 1908 to 2004) how many times did a third candidate actually get electoral votes?
It is more than I actually would have thought. Ten times out of 25 elections. A full 40% of the elections in that time period.
The ones with asterisks are cases where the third person got an electoral vote due only to a faithless elector. In all the other cases the third person actually “earned” the electoral votes.
(Or at least most of them… in a couple of cases faithless electors added to a third candidate’s total, but the candidate also got other electoral votes by the normal means… and the 1960 case was interesting too as some of the electors were actually directly elected as unpledged electors… some of whom voted for Byrd, who wasn’t actually running.)
Given that, you could discount 5 of those 10 elections. Even so, you are left with 5 elections (20% of the elections) where a third person “legitimately” earned electoral votes. Which is more often than I would have thought.
Now granted, while the last “faithless elector” incident was very recent… the 2004 election… the last time a third candidate actually “won” electors was 1968, a full 40 years ago. So we’re a bit overdue! It doesn’t look all that likely this time around, but perhaps in 2012. :-)
But maybe we could have a faithless elector or two. That could be fun. :-)
Brandy turned me on to this fun game. Well, Brandy’s version is a little different, but here are my rules.
Start with by clicking “Random Article” on Wikipedia. Then click the first link in each article (not counting standard navigation and disambiguation links and and such not counting pages you have already gone to) and just see where you travel.
OK, that’s 20, so I’m going to stop. OK, so maybe it wasn’t that much fun. Of course, in Brandy’s version she actually reads each of the pages and learns about whatever the subject matter is, and usually starts from a page she actually had some interest in rather than doing the random thing, but whatever. :-)
I’ve of couse spent many hours flipping between wikipedia pages before and ended on all sorts of tangents, and there is a famous cartoon about that… it is the “first link” thing that makes this different.
Yeah, OK, fine. Maybe the other way is better. :-)
