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1, 2, 3, 211, 5, 23, 7, 3331113965338635107, 311, 773, ... For n ≥ 2, a(n) is the prime that is finally reached when you start with n, concatenate its prime factors ...
Even and odd numbers: An integer is even if it is a multiple of 2, and is odd otherwise. Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]
For example, if this is session 0, boxes 0-2-5-9, 1-3-6-0, 5-7-0-4, and 8-0-3-7 are done because they all contain the number 0. If a reviewed card isn't successful, it moves back to Deck Current. If a reviewed card is successful and the last number of its box matches the current session number, then that card moves to the Retired Deck.
The following languages are listed as having at least 50 million first-language speakers in the 27th edition of Ethnologue published in 2024. [7] This section does not include entries that Ethnologue identifies as macrolanguages encompassing all their respective varieties, such as Arabic, Lahnda, Persian, Malay, Pashto, and Chinese.
Many properties of a natural number n can be seen or directly computed from the prime factorization of n.. The multiplicity of a prime factor p of n is the largest exponent m for which p m divides n.
21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2] [3]
The arrangement of digits on numeric keypads with the 7-8-9 keys two rows above the 1-2-3 keys is derived from calculators and cash registers. It is notably different from the layout of telephone Touch-Tone keypads which have the 1 - 2 - 3 keys on top and 7 - 8 - 9 keys on the third row.