Yes, I’ve been remiss. Being hospitalised does that to you. So it will take me a little time to catch up. Here’s what should have been the Friday question for the day I went into hospital in San Francisco.
What’s the next number in the sequence …. 31, 55, 332, 789…
As usual, do what you like. I have tried as hard as possible to make it ungoogleable.
9 thoughts on “The Friday Question: 22 June 2012”
Sorry to hear you have been unwell JP, hope you are making a speedy recovery:)
It’s a part of a Fibonnaci ananym sequence (a.k.a. Icannobif prime), which runs: 0, 1, 1, 2, 3, 5, 8, 12, 31, 43, 55, 98, 332, 441, 773, 789, 1814, 4852, 5676, 7951, 11771, 52057, 64901, 75682, 86364, 118713, 393121, 814691, 922415… though I have to admit I haven’t worked out why certain numbers are being skipped (first two skip one sequence number, then the last skips two) – so so far, at best, a guess that it’s going to be 5676 (skipping two again).
Almost. But googling that is the easy part. The hard part is explaining the gaps.
Given that the full sequence is right, the skips are 1 if the current number is odd, 2 if it’s even. So the next two numbers would be 4852, and 11771.
1814 is the correct answer by the way. I won’t say why. That’s JPs privilege, should he wish to divulge it :)
All I did was take plain old Fibonacci.
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 etc
then I dropped the single digit entries
then I flipped the numbers so they read 31 12 43 55 98 441 332 773 016 789 7951 4852 1814
*I did NOT reorder them*
and then I went 31 drop 2 55 drop 2 332 drop 2 789 drop 2 1814
I saw no reason to reorder the numbers once I’d reversed them. Why?
So it’s 1814.
Let me know if you disagree violently and if so why. I’d love to understand.
If I had a set of terms in sequence and I reversed each term, surely the reversed term should keep its place in the series. Because it’s the series, just with the terms reversed.
At least that’s how I envisioned it.
Happy to be shown otherwise. But at least you know there was method in my madness.
There are all sorts of ‘accepted’ Fibonacci related sequences and one branch of this involves reordering the reversed numbers. I think it’s called Fibinacci ananyms. In some cases the reversed number is used to derive numbers further along the sequence. In others the math stays the same but the results are just reordered. All a bit tenuous the more you shuffle things. Check out http://oeis.org/wiki/Main_Page
Anyway, it’s important here because Google finds your numbers in the sequence called Fibonacci ananym, only there are gaps between the numbers. Your 3rd and 4th numbers are 3 numbers apart, but the others only 2. Too random to be explained but enough of a clue that Fibonnaci and reversals played a role.
Deference means you end up looking for things that aren’t there, for things that are more complicated than they are. This is something I discovered I did a lot in my recent interviews. Confidence maybe.
In the end your numbers were simply reversed but not ordered.
In the sequence 0,1,1,2,3,5,8,12,31 it took me ages to figure out why 12 was there.
Your problem was cool because it moved things out of the question making googling harder. But not impossible :)
I think that given all the tenous sequences accepted into the OEIS you should submit reveresed Fibonacci as it’s not there at the moment!