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1: 2 2: 4 3: 8 4: 16 5: 32 6: 64 7: 128 8: 256 ... used to explicitly describe an eight bit sequence. ... enough to handle all the range of numbers a calculator can ...
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 ...
2, 4, 16, 64, 4096, 65536, 262144, 1073741824, ... (sequence A019279 in the OEIS). To illustrate: it can be seen that 16 is a superperfect number as σ(16) = 1 + 2 + 4 + 8 + 16 = 31, and σ(31) = 1 + 31 = 32, thus σ(σ(16)) = 32 = 2 × 16. If n is an even superperfect number, then n must be a power of 2, 2 k, such that 2 k+1 − 1 is a ...
Most modern lenses use a standard f-stop scale, which is an approximately geometric sequence of numbers that corresponds to the sequence of the powers of the square root of 2: f / 1, f / 1.4, f / 2, f / 2.8, f / 4, f / 5.6, f / 8, f / 11, f / 16, f / 22, f / 32, f / 45, f / 64, f / 90, f / 128, etc. Each element in the sequence is one stop ...
Knuth's up-arrow notation. In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. [ 1] In his 1947 paper, [ 2] R. L. Goodstein introduced the specific sequence of operations that are now called hyperoperations. Goodstein also suggested the Greek names tetration, pentation ...
The sequence of highly composite numbers (sequence A002182 in the OEIS) is a subset of the sequence of smallest numbers k with exactly n divisors (sequence A005179 in the OEIS ). Highly composite numbers whose number of divisors is also a highly composite number are. 1, 2, 6, 12, 60, 360, 1260, 2520, 5040, 55440, 277200, 720720, 3603600 ...
In mathematics, 1 + 2 + 4 + 8 + ⋯ is the infinite series whose terms are the successive powers of two. As a geometric series, it is characterized by its first term, 1, and its common ratio, 2. As a series of real numbers it diverges to infinity, so the sum of this series is infinity. However, it can be manipulated to yield a number of ...
The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 2 64 −1 or 18,446,744,073,709,551,615 (eighteen quintillion ...
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