What is the magic number sequence?

Asked by: Dr. Ian Connelly  |  Last update: March 14, 2026
Score: 4.6/5 (71 votes)

A magic sequence of length n is a sequence of integers x0… xn−1 between 0 and n−1, such that for all i in 0 to n−1, the number i occurs exactly xi times in the sequence. For instance, 6,2,1,0,0,0,1,0,0,0 is a magic sequence since 0 occurs 6 times in it, 1 occurs twice, etc.

Why are 2 8 8 18 18 32 called magic numbers?

The numbers 2, 8, 8, 18, 18, 32 are known as magic numbers. It is because of the fact that the elements which occur after these intervals have similar properties. For example, atomic number of Li is 3. If we add 8 (magic number) to 3, then we will get atomic number 11 which stands for sodium.

What is the magic number explained?

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. As a result, atomic nuclei with a "magic" number of protons or neutrons are much more stable than other nuclei.

Why is 82 a magic number?

Consider the incremental binding energies for the element Indium (atomic number 49). The sawtooth pattern is the effect of the formation of neutron-neutron spin pairs. The sharp drops after 50 and 82 neutrons are the result of the filling of neutron shells. Fifty and 82 are magic numbers.

What is the magic number theory?

magic number, in physics, in the shell models of both atomic and nuclear structure, any of a series of numbers that connote stable structure. The magic numbers for atoms are 2, 10, 18, 36, 54, and 86, corresponding to the total number of electrons in filled electron shells.

The magic of Fibonacci numbers | Arthur Benjamin | TED

38 related questions found

What is the magic number formula?

You can calculate the magic number for your SaaS business by subtracting the last quarter's annual recurring revenue (ARR) from the current quarter's ARR and dividing by your total customer acquisition cost (CAC) (your total sales and marketing spend) from the previous quarter.

Why is 137 a magic number?

To the world of physics, 137 is synonymous with the fine structure constant. This constant, represented as approximately 1/137.03599913, gauges the strength of the electromagnetic force, according to the National Institute of Standards and Technology.

What is the human magic number?

The "magical number 7" and working memory capacity

Chunking is used by the brain's short-term memory as a method for keeping groups of information accessible for easy recall.

Why is 69 a magic number?

69 is a lucky number because it is a natural number that remains after repeatedly removing every nth number in a sequence of natural numbers, starting from 1. In decimal, 69 is the only natural number whose square (4761) and cube (328509) use every digit from 0–9 exactly once.

Why 40 is a magical number?

In Biblical terms the numerical number 40 has significant meaning. Think of the 40 days and 40 nights of rain floods. It took the Israelites 40 years to find the Promised Land, and Jesus spent 40 days in the dessert before his crucifixion. Maybe it takes 40 years to grow into an awesome woman.

What is the most powerful magical number?

Seven was the most powerful magical number, based on centuries of mythology, science, and mathematics, and therefore had a very important role in the wizarding world. Arithmancer Bridget Wenlock was the first to note this through a theorem which exposed the magical properties of the number seven.

How do you find out your magic number?

Take the total number of games, e.g., 162. Subtract the total wins of the first team, e.g., 55. Subtract the losses of the second team, e.g., 57. Add 1 to the result and you have your first team's magic number, i.e., 51.

What is the magic code?

Magic code is a programming puzzle game, the game uses game mechanics firmly rooted in programming concepts. The game allows players to get a practical understanding of the basic concepts such as the sequence of instructions, procedures and cycles, learn the basics and logic of programming.

What is the real magic number?

The conventional magic numbers for the nucleus are {2, 8, 20, 28, 50, 82, 126}. The case is made elsewhere that 6 and 14 are also magic numbers. (A recent study also found evidence for a magic number of about 180.) Thus the magic numbers for filled shells are then {2, 6, 8, 14, 20, 28, 50, 82, 126}.

What is the 288 rule?

This rule, also known as the electronic structure rule, helps us grasp how electrons are arranged in atoms. It states that the first energy level can hold up to 2 electrons, while the second and third levels can each accommodate up to 8 electrons.

Why do people say 3 is the magic number?

Throughout human history, the number 3 has always had a unique significance, but why? The ancient Greek philosopher, Pythagoras, postulated that the meaning behind numbers was deeply significant. In their eyes the number 3 was considered as the perfect number, the number of harmony, wisdom and understanding.

Why is 69 forbidden?

No NBA player has ever worn the number 69, which is believed to be implicitly banned due to its sexual connotations; the NBA has never confirmed this. Dennis Rodman allegedly requested the number 69 when he joined the Dallas Mavericks but was refused and instead wore 70.

What is my angel number?

Just add up the numbers in your birthdate, month, and year. If you get a big number, add those numbers together until you have a single number. For example, if you're born on March 7th, 1997, add 0 + 3 + 0 + 7 + 1 + 9 + 9 + 7, which is 36. Then, add 3 + 6 to get 9. That's your angel number!

Who is the forbidden number 69?

Out of all the numbers that have been worn by players in NBA history, the No. 69 hasn't been worn by anyone in the league. The reason behind this is because the number is used to refer to a sexual position. Being a family-friendly league, the NBA decided to ban the number from being worn by any player.

What is most powerful number in the world?

144000 is a powerful number. Every exponent in its prime factorization is larger than 1. It is the product of a square and a cube. A powerful number is a positive integer m such that for every prime number p dividing m, p2 also divides m.

What is the secret number of the universe?

42 is the number with which God creates the Universe in Kabbalistic tradition. In Kabbalah, the most significant name is that of the En Sof (also known as "Ein Sof", "Infinite" or "Endless"), who is above the Sefirot (sometimes spelled "Sephirot").

What number is the secret to life?

Douglas Adams said it was the answer to the meaning of life, the universe, and everything. He meant it as a joke, but a new book shows how the number 42 has played a significant role in history.

Why is 11 11 a magic number?

In numerology, the angel number 1111 carries significant meaning. According to The Law of Attraction, it represents a gateway to spiritual awakening and enlightenment. The repetition of the number 1 amplifies its energy, symbolizing new beginnings, manifestation, and the connection between thoughts and reality.

What is the most mystical number?

Jungian psychology and mysticism

137 has been the subject of psychological speculation by Swiss psychiatrist and psychoanalyst Carl Jung concerning his theory of synchronicity.

What is a pure number?

Numbers that exist purely as numbers and do not represent amounts of quantities are called pure numbers.