Produce the recursive version of the following iterative code. Also find T (n ) and S (n). for (int x-0;x
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- Question: Let t(x) be the number of primes that areThe Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…Write a recursive function that takes an array and a callback function and returns True if any value of that array returns True from that callback function otherwise returns False.As a callback funtion for this problem, assume that the callback function is used to check if a given input is an even number.- Analyse the running time of the algorithmWrite a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, then the pattern generated is: **** *** ** * ** *** ****Give a recursive definition for the set POWERS-OF-TWO = {1 2 4 8 16 ....} and use your definition to prove that the product of two POWERS-OF-TWO is also a POWER-OF-TWOLet F be the function such that F(n) is the sum of the first n positive integers. Give a recursive definition of F(n).Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. Sierpinski.java When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle with the specified side length. public static double height(double length) // Draws a filled equilateral triangle with the specified side length // whose bottom vertex is (x, y). public static void filledTriangle(double x, double y, double length) // Draws a Sierpinski triangle of order n, such that the largest filled //…Find a recursive definition for the sequence 5, 7, 10, 14, 19,... for n>1. How do I find the equation/recursive definition for this?Show that f(x, y) = x +y is primitive recursive.Write a recursive function body to find the nth term of Fibonacci Series. [Write only recursive function body . No need of main ( ) code ] int fib(int x) {….. …… }Flip a fair coin repeatedly until you get two heads in a row (HH). What is the probability of getting HH in at-most N (N > 1) tosses? Can you write a recursive function and implementation to calculate the probability?Let E(x) = 1 if x is a multiple of 3, E(x) = 0, otherwise. Show that E(x) is primitive recursive.SEE MORE QUESTIONS