1. A

    Having Sum Fun Counting Ordinals

    This is a draft. Knowing me, it is probably nonsensical and filled with errors. I'm trying to enumerate some very large countable ordinal assuming of course that math isn't broken and I can't enumerate $\omega_1$ itself. ... And no, jic, I don't think math is broken. Why? Do you? :spin...
  2. Y

    prime counting function

    pi(n) = n/ln(n) + n/ln^2(n) + n/ln^3(n) + ... I think this is stronger than prime number theorem and closer to the true value of pi(n).
  3. Y

    result of my prime counting function

    pi(n) = number of primes less than n i proved that: pi(n) - pi(√n) = n × (1/2 × 2/3 × ... × p-1/p) p = largest prime less than or equal to √n prime number theorem: pi(n) = n/ln(n) lim pi(√n) / pi(n) = lim √n/ln(√n) / n/ln(n) = lim 2/√n = 0 => pi(n) - pi√n ~ pi(n) = n ×...
  4. Z

    Counting real numbers

    To count the real numbers in [.1,1), remove the decimal point.
  5. H

    Words counting and ranking

    Hi everyone, Can you support me to solve this problem; All words which contain 2,3,4, or 5 English letters (A to Z) are listed alphabetically. In each word, the letters can be repeated, but any two adjacent letters must be distinct. So, the first word is "AB", and the last one is "ZYZYZ"...
  6. J


    The question is “in how many possible ways can 8 identical balls be distributed to 3 distinct boxes so that every box contains at least one ball?” There is a hint saying that the case can be considered as putting two bars on a row of eight balls, like o o l o o o l o o o the answer is...
  7. C

    Prime counting. Meissel, Lehmer: is there a general formula?

    I am looking for a general formula to count prime numbers on which the Meissel and Lehmer formulas are based: $$\pi(x)=\phi(x,a)+a-1-\sum\limits_{k=2}^{\lfloor log_2(x) \rfloor}{P_k(x,a)}$$ Wiki - prime counting - Meissel Lehmer More precisely, I am looking for the detailed description of...
  8. D

    Counting Problem

    What power of p divides (p^a)*m "choose" p^a?
  9. T

    Counting Functions

    Hi: I'm trying to understand counting functions between two sets. For example, between two 3-element sets, there are 3^3=27 functions. And there are 3!/0!=6 one-to-one functions. What are the other 21 functions? Thayer
  10. C

    Counting Prin. & Binomial T.

    So, I'm trying to focus heavily on mastering this topic for my upcoming meet. This is a 5-point question, and I have yet to understand the process to get to the answer. Question: Find the number of positive integers less than 10,000 with all distinct digits. Any possible ideas? Also...
  11. P

    counting problem

    If $n$ persons are sitting around a table $(n\geq 4)$, then the number of arrangements in which all shall not have same neighbours is
  12. J


    I have 3 distinguishable balls and two boxes labeled box 1 and box 2. How many different ways can I put the 3 balls into the 2 boxes? Thanks
  13. S

    The relationship of Counting number field & Prime numbers

    Counting number field (1,2,3,....) results into consequences such as for example prime numbers. Prime numbers are located in the counting number filed (1,2,3,4,5,6,7,8,9,10,11,...). The bolded numbers are primes. So we can assume that the counting number field has a great relationship to PN that...
  14. P

    Doubt in Counting

    How many numbers in the range 1000 -9999 do not have any repeated digit? In solution how many ways that we can select a digit at 1's place and 10's place , 100's and 1000's .then we multiply them Consider selecting each digit at particular place is an event so My question is Are...
  15. S

    What is Relationship between $\zeta(s)$ and Simple Prime-Power Counting Function?

    Assume the following definitions: $\zeta(s)$ - Riemann zeta function $\zeta'(s)$ - first-order derivative of the Riemann zeta function $\vartheta(s)$ - first Chebyshev function $\vartheta'(s)$ - first-order derivative of the first Chebyshev function $\psi(s)$ - second...
  16. B

    Twin Prime counting function & Euler constant

    Hi everyone! I am new to the forum. In my spare time, I've been trying to find a way to count twin primes under any given x. I know there is a method that exists that utilizes the Twin Prime Constant. Anyways, I found the distribution of twin primes to be related to the Euler-Mascheroni...
  17. S

    Fourier Series for Prime Counting Functions

    If you're interested in prime number theory and the Riemann hypothesis, you'll probably be interested in the following website which illustrates Fourier series for several prime counting functions and their first and second-order derivatives. Probably the most interesting result illustrated is...
  18. M

    Counting the number of powers

    A power is defined as number n >0 power to k with k>=2 P(10)=4 (1,4,8,9) P(10^50)=? P() represents the counting function of powers.
  19. D

    a problem related to the counting principle

    Suppose that you want to make license plates that consist of three letters followed by three digits. The letters can be chosen from A to Z and the digits can be chosen from 0 to 9. You are allowed to use the same letter twice and the same number twice. How many license plates can you make...
  20. M

    Combinatorics : counting

    Hi, We have a grid 6x6. We want to place on each square one of 36 tokens. 18 tokens are red : 6 copies of tokens numbered from 1 to 3. 18 tokens are blue : 6 copies of tokens numbered from 1 to 3. In how many different ways could we place them all? Thank you. Ps : It is not a...