Math Is Fun Forum

ecinreb

Member

Registered: 2015-07-09

Posts: 1

Mathematical Sequence Puzzle

What is the formula for the sequence below numbers moving from left to right per line of 7 numbers

16      18      20      21      23      39      31
21      4       33      22      38      24      19
3       48      23      37      40      5       2
10      24      43      35      23      36      37
34      28      22      12      14      32      15
28      4       48      45      44      39      12
3       39      5       23      43      36      45
32      18      42      37      6       28      39
22      39      16      4       1       10      13
5       6       2       7       8       37      48
30      23      39      48      5       26      47

mathaholic

Member

From: Earth

Registered: 2012-11-29

Posts: 3,251

Re: Mathematical Sequence Puzzle

Hmm... Lemme give it a try. First line: n + 2 + 2 + 1 + 2 + 16 - 8?

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Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mathematical Sequence Puzzle

If you mean the whole thing, I think it's clear there is no simple formula. It's a complete mess. Even the best polynomial of degree ten is an awful fit that accounts for only 27.8% of the variation, which was calculated at desmos.com as approximately:
f(n) = 2.6039·10^-14 n^10 - 9.4352·10^-12 n^9 + 1.5318·10^-9 n^8 - 1.4057·10^-7 n^7 + 0.00000767 n^6 - 0.00024247 n^5 + 0.0038791 n^4 - 0.012534 n^3 - 0.44326 n^2 + 5.0707 n + 10.41
A simpler rule with 5.64% accuracy is -0.0085213 n^2 + 0.5386 n + 19.183
A graph of this is given here: https://www.desmos.com/calculator/u4ccy8dlay

But then, you could say the same about the Fibonacci sequence, and that has a formula of sorts. At any rate, though, I sure can't see one

Last edited by Relentless (2015-12-16 08:00:49)

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mathematical Sequence Puzzle

Having had some practice recently with constructing polynomials, I suppose I will come back here from time to time to construct rules for these seemingly random sequences for more practice.

A rule for the first line is the following:

So the series continues: ...39, 31, -222, -1326, -4544 haha

Last edited by Relentless (2015-12-30 03:45:52)

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mathematical Sequence Puzzle

A polynomial that describes the second line:

The series continues: ...24, 19, 875, 5471, 20424...