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  2. Knuth's up-arrow notation - Wikipedia

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

    Download as PDF; Printable version; ... the power tower might be written using dots and a note indicating the height of the tower. ... formula 1 2: 4: 8: 16: 32: 64 ...

  3. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    Graphs of y = b x for various bases b: base 10, base e, base 2, base ⁠ 1 / 2 ⁠. Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.

  4. Power of two - Wikipedia

    en.wikipedia.org/wiki/Power_of_two

    The only known powers of 2 with all digits even are 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^6 = 64 and 2^11 = 2048. [11] The first 3 powers of 2 with all but last digit odd is 2^4 = 16, 2^5 = 32 and 2^9 = 512. The next such power of 2 of form 2^n should have n of at least 6 digits.

  5. Wheat and chessboard problem - Wikipedia

    en.wikipedia.org/wiki/Wheat_and_chessboard_problem

    The number of grains of wheat on the second half of the chessboard is 2 32 + 2 33 + 2 34 + ... + 2 63, for a total of 2 642 32 grains. This is equal to the square of the number of grains on the first half of the board, plus itself. The first square of the second half alone contains one more grain than the entire first half.

  6. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    Exponentiation can be thought of as a chained multiplication involving numbers of and tetration as a chained power involving numbers . Each of the operations above are defined by iterating the previous one; [ 1 ] however, unlike the operations before it, tetration is not an elementary function .

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  9. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...