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A108974 Sort the primes (except 2) according to the multiplicative order of 2 modulo that prime. If two primes have the same order of 2, they are arranged numerically. 5

%I

%S 3,7,5,31,127,17,73,11,23,89,13,8191,43,151,257,131071,19,524287,41,

%T 337,683,47,178481,241,601,1801,2731,262657,29,113,233,1103,2089,331,

%U 2147483647,65537,599479,43691,71,122921,37,109,223,616318177,174763,79

%N Sort the primes (except 2) according to the multiplicative order of 2 modulo that prime. If two primes have the same order of 2, they are arranged numerically.

%C Or, primitive prime divisors of the Mersenne numbers 2^n-1 (see A000225) in their order of occurrence.

%C Of course the Mersenne primes 2^p-1 (cf. A000043) appear in this sequence.

%H Charles R Greathouse IV, <a href="/A108974/b108974.txt">Table of n, a(n) for n = 1..4275</a>

%H G. Everest et al., <a href="http://www.jstor.org/stable/27642221">Primes generated by recurrence sequences</a>, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431.

%H K. Zsigmondy, <a href="https://doi.org/10.1007%2FBF01692444">Zur Theorie der Potenzreste</a>, Monatsh. Math., 3 (1892), 265-284.

%e The order of 2 modulo 3 is 2 and the order of 2 modulo 7 is 3. So 3 comes before 7.

%o (PARI) do(n)=my(v=List(),P=1,g,t,f); for(k=2,n, t=2^k-1; g=P; while((g=gcd(g,t))>1, t/=g); f=factor(t)[,1]; for(i=1,#f, listput(v,f[i])); P*=t); Vec(v) \\ _Charles R Greathouse IV_, Sep 23 2016

%Y Cf. A000225, A000043, A001348, A014664, A086251.

%K nonn

%O 1,1

%A Douglas Stones (dssto1(AT)student.monash.edu.au), Jul 27 2005

%E More terms from _Martin Fuller_, Sep 25 2006

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Last modified February 21 22:10 EST 2020. Contains 332113 sequences. (Running on oeis4.)