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A mnemonic is a memory aid used to improve long-term memory and make the process of consolidation easier. Many chemistry aspects, rules, names of compounds, sequences of elements, their reactivity, etc., can be easily and efficiently memorized with the help of mnemonics.
Regular paperfolding sequence: 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ... At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence. A014577: Blum integers: 21, 33, 57, 69, 77, 93, 129, 133, 141, 161, 177, ... Numbers of the form pq where p and q are distinct primes congruent to 3 (mod 4). A016105: Magic ...
Determining a general formula for the Pisano periods is an open problem, which includes as a subproblem a special instance of the problem of finding the multiplicative order of a modular integer or of an element in a finite field. However, for any particular n, the Pisano period may be found as an instance of cycle detection.
The form with the f-block included in the main body is sometimes called the 32-column [6] or long form; [33] the form with the f-block cut out the 18-column [6] or medium-long form. [33] The 32-column form has the advantage of showing all elements in their correct sequence, but it has the disadvantage of requiring more space. [34]
For these extreme cases, individual elements of decimal sequences immediately settle into a permutation of the form a0 b1 c2 d3 e4 f5 g6 h7 i8 j9 where here the letters a–j are placeholders for digit counts from the preceding sequence element. Since the sequence is infinite, and the length of each element is bounded, it must eventually repeat ...
The sequence of powers of −1 is periodic with period two: ,,,,, … More generally, the sequence of powers of any root of unity is periodic. The same holds true for the powers of any element of finite order in a group. A periodic point for a function f : X → X is a point x whose orbit
Informally, a sequence has a limit if the elements of the sequence become closer and closer to some value (called the limit of the sequence), and they become and remain arbitrarily close to , meaning that given a real number greater than zero, all but a finite number of the elements of the sequence have a distance from less than .
Here [Ne] refers to the core electrons which are the same as for the element neon (Ne), the last noble gas before phosphorus in the periodic table. The valence electrons (here 3s 2 3p 3) are written explicitly for all atoms. Electron configurations of elements beyond hassium (element 108) have never been measured; predictions are used below.