1. Aug 31, 2006

What is the next term of the given sequence..
1,4,9,61,52, 63, 94, 46, 18, 001, 121, 441, 961, 691, 522, 652, .....(?)

2. Aug 31, 2006

### BSMSMSTMSPHD

Is the tenth term supposed to be 001?

3. Aug 31, 2006

### bomba923

Yes, and Aladin just fixed it. Anyhow, each term simply represents perfect squares with digits reversed; thus the next term is 172 with digits reversed (i.e., 982). This thread probably belongs in h*ttp://www.physicsforums.com/forumdisplay.php?f=33

Last edited: Aug 31, 2006
4. Aug 31, 2006

### mtanti

Yes it is supposed to be 001! What is happening is that you are finding the square numbers and reversing the order of digits! So the next number would be 982.

Piece of cake...

5. Aug 31, 2006

### quasar987

haha, nice one mtanti!

6. Aug 31, 2006

### mathwonk

according to the lagrange interpolation theore, any finite number of n numbers can be the first n elements of a sequence defiuned by a polynomial of degree at most n-1, so there is no way to guess the formula for a given sequence unless you specify that the formula is a polynomial of degree at most n-1.

e.g. the sequence 2,4,6,8, is obtained not just from the formula a(n) = 2n, for n=1,2,3,4, but also from the formula a(n) =

2(x-2)(x-3)(x-4)(x-5)/(1-2)(1-3)(1-4)(1-5)

+ 4(x-1)(x-3)(x-4)(x-5)/(2-1)(2-3)(2-4)(2-5)

+6(x-1)(x-2)(x-4)(x-5)/(3-1)(3-2)(3-4)(3-5)

+8(x-1)(x-2)(x-3)(x-5)/(4-1)(4-2)(4-3)(4-5)

+11(x-1)(x-2)(x-3)(x-4).

but this foprmula gives a(5) = 11, instead of 10.

so what is lagrange's IQ?

7. Sep 1, 2006

### HallsofIvy

And what does guessing what answer you wanted have to do with IQ?

Here's an easier one: If you mark the circumference of a circle with n points, NOT equally spaced, and draw all lines connecting them, you divide the face of the circle in to areas (the purpose of "NOT equally spaced" is that no more than 2 lines cross at a point so you get the maximum possible number of areas). With 1 point, one area; 2 points, 2 areas; 3 points, 4 areas; 5 points, 8 areas; 9 points, 16 areas. How many areas do you get with 6 points? (there is a simple formula.)

8. Sep 1, 2006

### CRGreathouse

http://www.research.att.com/~njas/sequences/A002942 [Broken]

http://www.research.att.com/~njas/sequences/A000127 [Broken]

Last edited by a moderator: May 2, 2017
9. Sep 1, 2006

Mtanti ! are you sure that the next term is 982.If it is right then how did you find this ?please tell me.

10. Sep 1, 2006

### mathwonk

IQ test: i am a 64 yer old math prof, with brown hair, and arthritis. i like to blog on physics forums and read comic books. my favorite wines include lescours "L", beychevelle, terrabianca campaccio, and ???? [what wine am i thinking of?]

11. Sep 1, 2006

### bomba923

Last edited: Sep 1, 2006
12. Sep 3, 2006

### the_next_einstein

ans

982 must b.squares in reverse

13. Sep 7, 2006

### mtanti

Hey! I had no idea about that! At first I thought about squares with modulo arithmetic as it was evident that it involved squares from the first few terms. Then I started seeing 61 and 18 and I started suspecting the reverse thing... So I tried it myself on my calculator and started revealing the sequence!

14. Sep 7, 2006

### bomba923

uhh sure...

And neither did (about three days later)
:uhh:

Last edited: Sep 7, 2006
15. Sep 8, 2006

### uart

Ha trick question. The answer is beer!