A225721 - OEIS

A225721

Starting with x = n, the number of iterations of x := 2x - 1 until x is prime, or -1 if no prime exists.

-1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 6, 1, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 8, 3, 1, 2, 1, 0, 2, 5, 1, 0, 1, 0, 2, 1, 2, 0, 583, 1, 2, 1, 1, 0, 1, 1, 4, 1, 2, 0, 5, 0, 4, 7, 1, 2, 1, 0, 2, 1, 1, 0, 3, 0, 2, 1, 1, 4, 3, 0, 2, 3, 1, 0, 1, 2, 4

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OFFSET

1,8

COMMENTS

This appears to be a shifted variant of A040076. - R. J. Mathar, May 28 2013

If n is prime, then a(n) = 0. If the sequence never reaches a prime number (for n = 1) or the prime number has more than 1000 digits, -1 is used instead. There are 22 such numbers for n < 10000.

LINKS

Christian N. K. Anderson, Table of n, a(n) for n = 1..10000

EXAMPLE

For a(20), the trajectory is 20->39->77->153->305->609->1217, a prime number. That required 6 steps, so a(20)=6.

PROG

(R)

y=as.bigz(rep(0, 500)); ys=rep(0, 500);

for(i in 1:500) { n=as.bigz(i); k=0;

while(isprime(n)==0 & ndig(n)<1000 & k<5000) { k=k+1; n=2*n-1 }

if(ndig(n)>=1000 | k>=5000) { ys[i]=-1; y[i]=-1;

} else {ys[i]=k; y[i]=n; }

}