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The Numerology Problem

Can you figure out the special significance of the following sequence?   (2, 6, 10, 15, 19)


The words "Numerology" and "special significance" in the statement of the problem should have given you a hint that this was not a simple mathematical problem.

The sequence (2, 6, 10, 15, 19) corresponds to every fourth floor starting from 2 in the building where I live. As you can see in the picture of the elevator panel, the number 13 is skipped to avoid "bad luck".

Elevator Buttons

If you did not guess the answer, it is because numerology is not mathematics. Numerology is defined as the study of the "occult meanings" of numbers and their supposed influence on human life. Almost every culture has superstitions and traditions about numbers that are reflected in their art, religion, folklore, and architectural designs. Numerology associates numbers with various attributes, e.g., lucky, unlucky, auspicious, or evil.

Even if we don't believe in the superstitions of numerology, we have to deal with the numerical traditions of our culture.

Learn more about Numerology

- Reader Nour Armany submitted the following comment:
I think there is a solution for the sequence 2, 6, 10, 15, 19, ...
It will be dependent on the relation between 2 sequences.

The first sequence is: 22, 32, 42, 52, 62, ...

The second sequence is: 2, 3, 6, 10, 17, ..., where each number depends on the addition of the two numbers before + 1.
So, 6=(2+3)+1, and so on.
[a modified Fibonacci series, Fn = Fn-1 + Fn-2 + 1]

The numbers in the puzzle sequence can be generated by subtracting the numbers of the second sequence from the corresponding numbers of the first sequence.

Using this logic, we will find out that the next number is 21. [72 - 28]

- Reader Sam Rushworth submitted the following comment:
... for any sequence such as this there are in fact infinitely many mathematical solutions even if you just consider polynomial fits. In this case the most simple such solution is shown below:

If Y is the Xth term in the sequence
  then Y=(-3X4 + 34X3 - 129X2 + 290X - 144)/24

This will produce the sequence 2,6,10,15,19,17,1 after which point it gets very negative very quickly but all terms are integers.
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