I’m copying below a clean copy of my latest C program to find some (but not all) record breaking values of the modified total stopping time to reach ‘1’, based on a small variant of the Lagarias total stopping time function sigma_{oo} (n), for integers n at least two, introduced by Jeffrey Lagarias in his 1985 American Mathematical Monthly “cyclopedic” article.
The program now uses two long long int integers to store intermediate (non-printed) computations, due to “blow-up” in the iterates of the T(.) function, following Lagarias1985.
The two long long int values are stored in a one-dimensional array of size 2. This functions in the code below as “arithmetic modulo 10^15 ” , and is defined in the first line of code with the token ‘MOD’.
Only integers n such that n == 27 (mod 100) are tested. This is a purely empirical criterion, that still appears to catch a healthy proportion of all “record-breaking” n.
David Bernier
Quebec City,
August 16, 2014
12:30 AM
#define MAX 100000000000
#define MOD 1000000000000000
#include <stdio.h>
int main(void)
{
long long n;
long long y[2];
long long steps;
long long maxsteps;
long long modulo2;
long long tmp;
long long ret;
maxsteps = 0;
for(n=27; n< MAX; n=n+100)
{
y[0] = n;
y[1] = 0;
steps = 0;
while(y[0]>1 || y[1]>0)
{
modulo2 = y[0]%2;
if(modulo2 == 0)
{
tmp = y[1]/2;
if(0 == (y[1]%2))
{
y[1] = tmp;
y[0] = y[0]/2;
}
else
{
y[1] = tmp;
y[0] = y[0] + MOD;
y[0] = y[0]/2;
}
}
else
{
y[1] = y[1]+y[1]+y[1];
y[0] = y[0]+y[0]+y[0];
y[0] = y[0]+1;
tmp = y[0]%MOD;
ret = (y[0]-tmp)/MOD;
y[1] = y[1] + ret;
y[0] = tmp;
}
steps++;
}
if(steps > maxsteps)
{
if(maxsteps< 1050)
{
maxsteps = steps;
}
printf(“%lld %lld total steps\n”, n, steps);
}
}
return 0;
}
