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  2. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

    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 ]

  3. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Name First elements Short description OEIS Mersenne prime exponents : 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, ... Primes p such that 2 p − 1 is prime.: A000043 ...

  4. List of numeral systems - Wikipedia

    en.wikipedia.org/wiki/List_of_numeral_systems

    This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters.

  5. English numerals - Wikipedia

    en.wikipedia.org/wiki/English_numerals

    Alternatively, and for greater numbers, one may say for 1 ⁄ 2 "one over two", for 5 ⁄ 8 "five over eight", and so on. This "over" form is also widely used in mathematics. Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 14 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths"

  6. List of conversion factors - Wikipedia

    en.wikipedia.org/wiki/List_of_conversion_factors

    1 ft/(h⋅s) = 8.4 6 × 10 −5 m/s 2: foot per minute per second: fpm/s ≡ 1 ft/(min⋅s) = 5.08 × 10 −3 m/s 2: foot per second squared: fps 2: ≡ 1 ft/s 2 = 3.048 × 10 −1 m/s 2: gal; galileo: Gal ≡ 1 cm/s 2 = 10 −2 m/s 2: inch per minute per second: ipm/s ≡ 1 in/(min⋅s) = 4.2 3 × 10 −4 m/s 2: inch per second squared ...

  7. Divisibility rule - Wikipedia

    en.wikipedia.org/wiki/Divisibility_rule

    Answer: 7 × 1 + 6 × 10 + 5 × 9 + 4 × 12 + 3 × 3 + 2 × 4 + 1 × 1 = 178 mod 13 = 9 Remainder = 9 A recursive method can be derived using the fact that = and that =. This implies that a number is divisible by 13 iff removing the first digit and subtracting 3 times that digit from the new first digit yields a number divisible by 13.

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  9. Knuth's up-arrow notation - Wikipedia

    en.wikipedia.org/wiki/Knuth's_up-arrow_notation

    The sequence starts with a unary operation (the successor function with n = 0), and continues with the binary operations of addition (n = 1), multiplication (n = 2), exponentiation (n = 3), tetration (n = 4), pentation (n = 5), etc. Various notations have been used to represent hyperoperations.

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