A new coin could be created using generation of the digits of pi as measure of computational work.Pi is an irrational number and can be written as generalised continued fraction as --
Recursive function implementing 1st continued fraction for n iterations
float rec(float x,int n){
float ret;
if(x>=n)
ret=1;
else
ret=(1+2*x)+((x+1)*(x+1)/rec(x+1));
return(ret);
}
int main(){
float x;
x=4/(1+(1/rec(1,8))); //here n=8
printf("\npi=%f",x);
return(0);
}
Here 8 iterations produce first 3 correct digits of pi.
It can be seen that as the number of iterations are gradually increased,computational complexity increases exponentially.Block reward could be adjusted accordingly.
Verification of n th digit can be directly found using
Bailey–Borwein–Plouffe formula. The formula can directly calculate the value of any given digit of pi without the need to calculate the preceding digits.
Attempt and result of obtaining 10 Trillion digits of pi
