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"subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence.
The look-and-say sequence is also popularly known as the Morris Number Sequence, after cryptographer Robert Morris, and the puzzle "What is the next number in the sequence 1, 11, 21, 1211, 111221?" is sometimes referred to as the Cuckoo's Egg , from a description of Morris in Clifford Stoll 's book The Cuckoo's Egg .
The complete sequences include: The sequence of the number 1 followed by the prime numbers (studied by S. S. Pillai [3] and others); this follows from Bertrand's postulate. [1] The sequence of practical numbers which has 1 as the first term and contains all other powers of 2 as a subset. [4] (sequence A005153 in the OEIS)
For integer k ≥ 3, an AP-k (also called PAP-k) is any sequence of k primes in arithmetic progression. An AP-k can be written as k primes of the form a·n + b, for fixed integers a (called the common difference) and b, and k consecutive integer values of n. An AP-k is usually expressed with n = 0 to k − 1.
An integer sequence is computable if there exists an algorithm that, given n, calculates a n, for all n > 0. The set of computable integer sequences is countable.The set of all integer sequences is uncountable (with cardinality equal to that of the continuum), and so not all integer sequences are computable.
Pre-math skills (referred to in British English as pre-maths skills) are math skills learned by preschoolers and kindergarten students, including learning to count numbers (usually from 1 to 10 but occasionally including 0), learning the proper sequencing of numbers, learning to determine which shapes are bigger or smaller, and learning to count objects on a screen or book.
Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum.
Here the nth term in the sequence is the nth decimal approximation for pi. Though this is a Cauchy sequence of rational numbers, it does not converge to any rational number. (In this real number line, this sequence converges to pi.) Cauchy completeness is related to the construction of the real numbers using Cauchy sequences.