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  2. Odious number - Wikipedia

    en.wikipedia.org/wiki/Odious_number

    Except for 3, every Mersenne prime is odious, because its binary expansion consists of an odd prime number of consecutive nonzero bits. Non-negative integers that are not odious are called evil numbers. The partition of the non-negative integers into the odious and evil numbers is the unique partition of these numbers into two sets that have ...

  3. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    A k-cycle is a cycle that can be partitioned into k contiguous subsequences, each consisting of an increasing sequence of odd numbers, followed by a decreasing sequence of even numbers. [15] For instance, if the cycle consists of a single increasing sequence of odd numbers followed by a decreasing sequence of even numbers, it is called a 1-cycle.

  4. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal to zero. Thus a non-negative number is either zero or positive.

  5. Fermat number - Wikipedia

    en.wikipedia.org/wiki/Fermat_number

    In mathematics, a Fermat number, named after Pierre de Fermat (1607–1665), the first known to have studied them, is a positive integer of the form: = +, where n is a non-negative integer.

  6. Descartes number - Wikipedia

    en.wikipedia.org/wiki/Descartes_number

    In number theory, a Descartes number is an odd number which would have been an odd perfect number if one of its composite factors were prime.They are named after René Descartes who observed that the number D = 3 2 ⋅7 2 ⋅11 2 ⋅13 2 ⋅22021 = (3⋅1001) 2 ⋅ (22⋅1001 − 1) = 198585576189 would be an odd perfect number if only 22021 were a prime number, since the sum-of-divisors ...

  7. Goldbach's weak conjecture - Wikipedia

    en.wikipedia.org/wiki/Goldbach's_weak_conjecture

    For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3). In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. [ 2 ]

  8. Leading zero - Wikipedia

    en.wikipedia.org/wiki/Leading_zero

    A leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. [1] For example, James Bond 's famous identifier, 007, has two leading zeros. [ 2 ] Any zeroes appearing to the left of the first non-zero digit (of any integer or decimal) do not affect its value, and can be omitted (or replaced ...

  9. Zero-based numbering - Wikipedia

    en.wikipedia.org/wiki/Zero-based_numbering

    Under zero-based numbering, the initial element is sometimes termed the zeroth element, [1] rather than the first element; zeroth is a coined ordinal number corresponding to the number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element ...