A number is "sneaky" if you finally reach ZERO. Example 1: Is 95 sneaky?
There are no valid solutions to the simultaneous equations resulting from some of the digits in {a,b,c,d} being equal. Therefore the number 6174 is the only number unchanged by Kaprekar's operation — our mysterious number is unique.
We know that 2, 3, 5, 7 are strange. They are the only 1 digit strange numbers. All 2-digit strange numbers must be made up of these digits and must be prime. An exhaustive search reveals that they are 23, 37, 53, 73 as all other 2-digit numbers with these digits are not prime.
Iterating this sum-of-squared-digits map always eventually reaches one of the 10 numbers 0, 1, 4, 16, 20, 37, 42, 58, 89, or 145 (OEIS A039943; Porges 1945). is said to be happy. For example, starting with 7 gives the sequence 7, 49, 97, 130, 10, 1, so 7 is a happy number.
Cynthia had a nice way of visualizing it. She suggested imagining all 100 numbers of the sequence in a line. We are ignoring the first 11 numbers, but they are still part of the sequence.
You can find a lot of 'happy numbers' such as: 310, 70, 86, 130, 7, 5555, 1212, 13, 1000 and other numbers which are variations of these, e.g. swapping the numbers the other way around (13, 31) and adding zeros onto the end of numbers (31, 310).
The distinct combinations of digits that form 10-happy numbers below 1000 are (the rest are just rearrangements and/or insertions of zero digits): 1, 7, 13, 19, 23, 28, 44, 49, 68, 79, 129, 133, 139, 167, 188, 226, 236, 239, 338, 356, 367, 368, 379, 446, 469, 478, 556, 566, 888, 899. (sequence A124095 in the OEIS).
1.618. The so-called Golden Number or phi defines a ratio that appears repeatedly in nature, for example in the way many flowers' petals are formed. Some claim it is also associated with beauty, although leading mathematicians insist this is not true.
The Fibonacci sequence is a famous group of numbers beginning with 0 and 1 in which each number is the sum of the two before it. It begins 0, 1, 1, 2, 3, 5, 8, 13, 21 and continues infinitely.
9. In contrast to 8, the number 9 often represents pain or sadness.
Simply put, pi is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.
Cool numbers are positive integers whose decimal representation contains only the cool digits 2 and 5. For example, numbers 25, 522, 2 are cool and 7, 15, 265 are not.
The first few weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, 10430, ... (OEIS A006037). An infinite number of weird numbers are known to exist, and the sequence of weird numbers has positive Schnirelmann density. (Sloane).
A powerful number is a positive integer m such that for every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a2b3, where a and b are positive integers.
One of the most important numbers in our universe is the number Pi or π. Explore humankind's odyssey—attempts throughout the ages that truly transcend cultures—to compute, approximate, and understand this enigmatic number.
The number 42 is especially significant to fans of science fiction novelist Douglas Adams' “The Hitchhiker's Guide to the Galaxy,” because that number is the answer given by a supercomputer to “the Ultimate Question of Life, the Universe, and Everything.”
Other examples of rare numbers are 65, 621770, 281089082, 2022652202, 868591084757, 872546974178 … (Sequence A035519 of OEIS). If we consider palindromic rare numbers, there are infinitely many rare numbers.
Select a three digit number in which the first and the last digit differ by at least two. Construct a second number by reversing the order of digits in the first.
The Golden Ratio (phi = φ) is often called The Most Beautiful Number In The Universe. The reason φ is so extraordinary is because it can be visualized almost everywhere, starting from geometry to the human body itself! The Renaissance Artists called this “The Divine Proportion” or “The Golden Ratio”.
It turns out the world's favorite number is seven — at least, according a recent survey with more than 44,000 participants from all over the world.
Numerology Number 5 is associated with the ruling planet Mercury. It is considered to be a good number that brings good luck in life, and those who belong to this number are intelligent, adventurous, and have good communication skills.
More than any other number, people seemed to pick 0 because they thought it was a clever thing to do, Bellos says. As for the world's “least favorite” number, that would be 110.
What are angel numbers? Angel numbers are repeating number sequences, often used as a guide for deeper spiritual exploration. These sequences can range from 000 to 999, and each has its own distinct meaning and energy. Is it in the stars? Free Daily and Monthly Horoscopes.
In some Christian numerology, the number 888 represents Jesus, or sometimes more specifically Christ the Redeemer. This representation may be justified either through gematria, by counting the letter values of the Greek transliteration of Jesus' name, or as an opposing value to 666, the number of the beast.
A strong number is a number where the sum of the factorials of its digits equals the original number. 1, 2, 145, and 40585 are some examples of Strong numbers.