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A number which is not happy is called sad or unhappy. More generally, a -happy number is a natural number in a given number base that eventually reaches 1 when iterated over the perfect digital invariant function for =. [1] The origin of happy numbers is not clear.
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
The secion, "Happy Primes" previously stated that adding 3 or 9 to 10 raised to a power always produces "Happy" numbers. However, 4 (= 10 0 + 3) is not.Further, the explanation for why 10 is Happy is flawed.
It is an octagonal number [1] and a happy number. [2] 133 is a Harshad number, because it is divisible by the sum of its digits. 133 is a repdigit in base 11 (111) and base 18 (77), whilst in base 20 it is a cyclic number formed from the reciprocal of the number three. 133 is a semiprime: a product of two prime numbers, namely 7 and 19.
A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.
a happy number. [3] palindromic in bases 3 (10001 3), 9 (101 9) and 40 (22 40). In science. The sixth magic number. References This page was last edited on ...
Twenty-eight is a harmonic divisor number, [4] a happy number, [5] the 7th triangular number, [6] a hexagonal number, [7] a Leyland number of the second kind [8] (), and a centered nonagonal number. [9] It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these). [10]
A surcomplex number is a number of the form a + bi, where a and b are surreal numbers and i is the square root of −1. [10] [11] ...