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

Offset: 1

Author

Kevin L. Schwartz and Christian N. K. Anderson, May 13 2013

Keywords

• sign

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.

Examples

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

Links

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

Crossrefs

Cf. A050921 (primes obtained).

Cf. A040081, A038699, A050412, A052333, A046069 (related to the Riesel problem).

Cf. A000668, A000043, A065341 (Mersenne primes), A000079 (powers of 2).

Cf. A007770 (happy numbers), A031177 (unhappy numbers).

Cf. A037274 (home primes), A037271 (steps), A037272, A037272.

Programs

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; }
}