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# [Math Game] The Four Fours

Kolyo

1
Wed 15 Jan, 2014 05:04 pm
@markr,
Z[ P(P( T(4) + P(4!!) )) ] = Z[ P(P(10*19)) ] = Z[9293]

Covers 8893 to 9603 because of the new Z[...] function described on p.6
markr

1
Wed 15 Jan, 2014 07:11 pm
@Kolyo,
Z[φ(P(P(P(√4))))^4] = Z[10^4] = Z[10000]

Covers 9600 to 10400 because of the new Z[...] function described on p.6
Kolyo

1
Thu 16 Jan, 2014 02:42 pm
@markr,
= Z[P(P(P(P([P(P(√4))]!!))) - 4!)] = Z[P(P(P(P(15))) - 4!)] = Z[P(P(211) - 4!)] = Z[P(1297 - 4!)] = Z[P(1273)] = Z[10,391]

Covers 9,991 to 10,791 because of the new Z[...] function described on p.6
0 Replies

Kolyo

1
Thu 16 Jan, 2014 04:57 pm
If anyone wants to join the game here's some Java code to give you the first however many values of the P(-) function. (Recall from earlier posts, that P(n) = the nth prime.) At present this just gives the first 2000 values of P(n). Change the "2000" to equal the number of primes you want.

Code:``` public class FigurePrimes { public static final int ORDER = 2000; public static void main(String[] args) { System.out.println("n\tnth prime\n---\t---\n1\t2"); int n = 3; for (int i=2; i<=ORDER; i++){ while (!isPrime(n)) n += 2; System.out.println(i + "\t" + n); n += 2; } } public static boolean isPrime(int n){ for (int d=2; d*d <= n; d++){ if (n%d==0) return false; } return true; } } ```

Also, FYI, φ(-) is Euler's totient function, and T(n) is the nth triangular number.
(Two other common functions we use.)
0 Replies

MattieSmith

1
Mon 20 Jan, 2014 07:44 pm
@Kolyo,
Can you give the formula how you get this answer? Thank you.
Kolyo

1
Mon 20 Jan, 2014 08:51 pm
@MattieSmith,
You want a formula for "5 = (4 * 4 + 4) / 4 " ?
(That's the content of the specific post that you replied to.)

Well, just remember PEMDAS for the order of arithmetic operations:
parentheses -> exponents -> multiplication & division -> addition & subtraction.

In the expression, first evaluate what's in the parentheses first, and do the multiplication before the addition, so we have: (4*4 + 4) = (16 + 4) = 20.
So we just have to divide that by 4 to get (4 * 4 + 4) / 4 = 20 / 4 = 5.
0 Replies

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