(PHP) MATHEMATICAL RESEARCH PROJECT

i need a skilled coder to write me a program in php which will compute values on the screen and transfer them into a grid. e.g suppose i ask u to make me a 3x3 grid with 9 numbers as follows. 1 2 3 4 5 6 7 8 9 this is a simple grid with the numbers increasing by 1 each time row by row. suppose i said make another one with starting value 1 and an increment of 2 using row by row logic it will look like 1 3 5 7 9 11 13 15 17 if i said draw a 2by2 grid with row by row doubling starting from 1 it would look like 1 2 4 8 3x3 would be 1 2 4 8 16 32 64 128 256 these are examples and not necessarily what i need. the program i need is more complex. Program ------------------ take any number and apply the following rules 1. If the number is EVEN divide it by 2. 2. if the number is ODD, multiply it by 3, then ADD 1 to the result, then divide this result by 2. 3. if the number is = 1, STOP. Rule 3 is important and our goal is to reach 1 when we reach 1 the program will stop executing. Example 1 (EVEN) suppose we start with x = 4. applying the rules will mean x = 4 is EVEN so rule 1 applies again and we go from 4 to 2 x = 2 is EVEN so rule 1 applies again and we go from 2 to 1 x = 1 so rule 3 applies and we STOP. the full sequence generated is {4,2,1} Total Elements in the sequence is 3. Total Iterations to reach the goal (=1) is 2. Note Total Iterations to reach 1 is always 1 less than total elements in the sequence. Special case of x =1 we are already at 1 so we stop (i.e not even start) so the sequence is technically {1} and the Iterations to reach goal is 0. Example 2: (ODD) x = 3. x= 3 is ODD so Rule 2 applies and 3 maps to (3(3) + 1) / 2 = (10/2) = 5 x= 5 is ODD so Rule 2 applies and 3 maps to (3(5) + 1) / 2 = (16/2) = 8 x= 8 is EVEN so Rule 1 applies and 8 maps to (8) / 2 = 4 x= 4 is EVEN so Rule 1 applies and 8 maps to (4) / 2 = 2 x= 2 is EVEN so Rule 1 applies and 8 maps to (2) / 2 = 1 x= 1 so Rule 3 applies and we STOP. Sequence generated = {3,5,8,4,2,1} Total Elements in the sequence is 6. Total Iterations to reach the goal (=1) is 5. Your job write a phpscript which will 1. ask for a starting number x (e.g 3) 2. ask for a GOAL (default is 1) 3. compute the iterates i.e. 5,8,4,2,1 using the 3 rules above 4. STOP the program when the GOAL is reached 4. output the sequence of iterates on the screen 5. output total number of iterations to reach 1. e.g suppose i enter 3 into the box and press RUN then the program will run and the output will be Sequence for x= 3: {3,5,8,4,2,1} Iterations to reach Goal (=1): 5 Note: id like u to allow me to alter the rules too, example EVEN RULE x -> x/2 by default but i might decide to make it x-> 2x so we would have a box and i can enter a scalar multiple example 2 or 0.5 similarly for ODD RULE we can have a box to enter 2 values e,g the odd rule is 3X +1 / 2 i could say 7X + 5 or 11X + 7 / 2 so theres 3 values can be modified the general formula is (AX + B) / C. i am free to choose any A,B,C default will be A=3 B=1 C=2 Regards. PLEASE NOTE i will need further work done on this so please if u do this properly i can give u more work We can store answers in the DB also if we want. for research and to study the numbers