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

1,8

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; }
}

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.

Sequence in context: A328620 A257510 A305445 * A040076 A019269 A204459

Adjacent sequences: A225718 A225719 A225720 * A225722 A225723 A225724

Keyword

sign

Author

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

Status

approved