Numbers enthusiasts will be looking at the new year with a touch of sadness. Another perfect square like 2025 (45)2 = 2,025) will not occur again until 2116 (46)2 = 2,116). The year 2027 will be a prime number. By comparison, our current year, 2026, seems almost boring. But this is a misconception.
Online Encyclopedia of Integer Sequences (OEIS), a kind of Wikipedia for numbers, with over 200 entries for “2026”. This means that the number appears in more than 200 number sequences. Some of these entries are quite vague For non-experts, such as those who depend on an understanding of the five-cell von Neumann neighborhood. Luckily the OEIS reveals many of the more accessible and amusing mathematical oddities associated with the number 2,026.
Among other things, 2,026 belongs to the group of almost prime numbers because it has only 1, 2, 1,013 and 2,026 as divisors – the chance of having a prime number is very small. It can also be used to generate prime numbers. It’s part of a sequence which collects prime numbers of the form 50…077 Thus, 577, 5077, 50077 and 5000077 are prime numbers, A prime number in this sequence is 5 × 102026 + 77—that is, 5 followed by 2,026 zeros and 77.
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Magnetic Towers of Hanoi
The number 2,026 belongs to the expansion of the classic mathematical game Tower of Hanoi. In the original game, there are three pillars holding different sized discs, each with a hole in the center. At the beginning of the game, the discs are placed on the first pole from largest to smallest, starting with the widest at the bottom. The goal is to get to the last pole by arranging all the disks in the same order – but each disk can only be placed on the larger disk, never on the smaller disk. It can be proved that the game can be solved n Disks require at least 2n – 1 move.
Many variations of this puzzle exist. In one particularly popular version, the discs are magnetic, with the upper part representing the north pole and the lower part representing the south pole. When you move a disk from one rod to the other, you reverse its direction: the north pole is then at the bottom. And since the poles repel each other, you now not only have to make sure that one disc can be placed on top of another depending on its size, but you also have to make sure that the orientation of the discs is correct. This makes the puzzle very difficult to solve.
as it turns out, Starting with eight discs, you need at least 2,026 moves. To solve the magnetic version of the Towers of Hanoi. (In contrast, if you start with three discs, you can solve the puzzle in just 11 moves.)
An unlucky year?
Superstitious readers should skip this section. The year 2026 may prove unlucky – at least for those paying attention frequency of friday the 13th,
Every calendar year has at least one month in which the 13th falls on a Friday – but never more than three. And 2026 is one of those years in which three months: February, March, and November have Friday the 13th.
This frequency last occurred in 2015. If you don’t remember all the terrible things that happened that year, Wikipedia offers List of natural disasters Which happened. Let’s hope the 2026 list will be shorter.
a happy number
To end on a positive note, it should be mentioned that 2026 is a so-called happy number, as popularized by the British mathematician Reginald Allenby. Although there are an infinite number of happy numbers, there are also an infinite number of sad numbers. To find out which category a number belongs to, you first need to square the individual digits of that number and then add them together. That calculation for 2,026 is 2² + 0² + 2² + 6² = 44.
You then repeat this calculation with the result 4² + 4² = 32, calculate again with that result and then repeat the calculation twice. This gives you the results 13, 10 and 1. The number 1 is the end point of calculation, and it characterizes a happy number: According to the above calculation, any number that ultimately ends in 1 is called happy.
On the other hand, tragic numbers like 37 have a different fate. For example, the calculation for 37 is 3² + 7² = 58. Continuing the calculations from this result, you arrive at 89, 145, 42, 20, 4, 16 and finally come back to 37. Thus tragic numbers get caught in a loop from which there is no escape. The only way this calculation can end is if it eventually reaches the number 1.
This article was originally published in spectrum der wissenschaft And was reproduced with permission.
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