cp's OEIS Frontend

A225721 Starting with x = n, the number of iterations of x := 2x - 1 until x is prime, or -1 if no prime exists.

%I A225721 #22 Sep 17 2013 06:10:33
%S A225721 -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,
%T A225721 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,
%U A225721 2,1,1,0,3,0,2,1,1,4,3,0,2,3,1,0,1,2,4
%N A225721 Starting with x = n, the number of iterations of x := 2x - 1 until x is prime, or -1 if no prime exists.
%C A225721 This appears to be a shifted variant of A040076. - _R. J. Mathar_, May 28 2013
%C A225721 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.
%H A225721 Christian N. K. Anderson, <a href="/A225721/b225721.txt">Table of n, a(n) for n = 1..10000</a>
%e A225721 For a(20), the trajectory is 20->39->77->153->305->609->1217, a prime number. That required 6 steps, so a(20)=6.
%o A225721 (R)
%o A225721 y=as.bigz(rep(0,500)); ys=rep(0,500);
%o A225721 for(i in 1:500) { n=as.bigz(i); k=0;
%o A225721     while(isprime(n)==0 & ndig(n)<1000 & k<5000) { k=k+1; n=2*n-1 }
%o A225721     if(ndig(n)>=1000 | k>=5000) { ys[i]=-1; y[i]=-1;
%o A225721     } else {ys[i]=k; y[i]=n; }
%o A225721 }
%Y A225721 Cf. A050921 (primes obtained).
%Y A225721 Cf. A040081, A038699, A050412, A052333, A046069 (related to the Riesel problem).
%Y A225721 Cf. A000668, A000043, A065341 (Mersenne primes), A000079 (powers of 2).
%Y A225721 Cf. A007770 (happy numbers), A031177 (unhappy numbers).
%Y A225721 Cf. A037274 (home primes), A037271 (steps), A037272, A037272.
%K A225721 sign
%O A225721 1,8
%A A225721 _Kevin L. Schwartz_ and _Christian N. K. Anderson_, May 13 2013