What row of numbers comes next 1 11 21 1211 111221 312211 13112221?

Answer 1

413311

Answer 2

Another answer:

1113213211

The first row - 1 - contains one 1 -> 11

11 contains two 1's -> 21

21 contains one 2, one 1 ->1211

1211 contains one 1, one 2, two 1's ->111221

etcetera.

Building on that theory, it would go

111221 contains three 1's, two 2's, one 1-> 312211

312211 contains one 3,one 1,two 2's two 1's->13112221

13112221 contains one 1,one 3,three 2's, one 1,

therefore the next sequence of numbers would be ->1113213211

Note that even if this sequence was continued infinitely, you would never get 4 or more as a sequence, as this would require you to have two sets of the same number next to each other, which is impossible.

Although this sequence seems non-mathematical, it is actually possible to write a function that outputs it. It can be found at http://dheera.net/sci/sequence_sol.php The % function is an abstract algebra function defined, using modular arithmetic, as this: x%y is congruent to x (mod y). The function ABS(x) = |x| = {x (x>=0), -x (x<0)}. The variables R, N, and S are all dummy variables for summation.

This sequence doesn't SEEM non-mathematical. It IS non-mathematical. It is non-mathematical because the elements of the sequence are not even numbers, but just collections of numerals. Notice that the question asks "what row of numbers comes next", not "what NUMBER comes next". Technically, even that's incorrect, because it's a row of numerals, not a row of numbers. But it illustrates the fact that the "row of numbers" is not, itself, a number. It's just a collection of numerals with a specific (non-mathematical) rule for determining the next element.

The way the series is DEFINED is not mathematical. There may or may not be a formula that can duplicate this series, but the formula is not how the series is DEFINED. Moreover, the "formula" is not mathematical, as it uses non-mathematical functions like mod and abs (just because a function is available in some programming language doesn't make it a "mathematical" function). Furthermore, the use of dummy variables automatically calls the formula into question (dummy variables are something you put in when you can't make your formula work). But dummy variables or not, without the values of R, N, and S, no one can verify that the formula results in the series. And even if it could duplicate the series, I am positive that it could only do so for a finite number of iterations. And if the person who provided the formula would be kind enough to provide the values of ALL of the undefined terms, I could PROVE it.

I'm sorry, but the above poster shows a limited understanding of what constitutes mathematics. First: dummy variables are used all of the time in math. As a particular example that at least some will be familiar with, integrals use dummy variables. Any formula involving a summation is likely to use dummy variables. Second: Mod and Abs are mathematical devices that have been around far longer than computer programs. Absolute Value is even a continuous function defined on the real numbers(or complex if you'd like). Mod is generally used with integers, and is one of the most basic constructions in Abstract Algebra. Finally, as a point of contention with both previous posters, the sequence itself is mathematical. Counting is the most basic math, but it is certainly Math.

"Although this sequence seems non-mathematical" guy here. Obviously I agree with your repudiation of the poster between us, and I would like to add that the bit about the way the sequence defined being non-mathematical is wrong, too. As initially presented, the sequences is NOT defined, simply partially represented. I would, however, maintain that the definition later given (though it is not the only possible definition, and not the inherently "correct" one) is in fact non-mathematical. It contains semantic information that math can't really handle, and requires you to read the strings of digits in a fundamentally non-mathematical way.

Answer 3

1234566

Answer 4

123

Answer 5

1113213211

Answer 6

1113213211

Answer 7

Egged