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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. 6
 3, 7, 5, 31, 127, 17, 73, 11, 23, 89, 13, 8191, 43, 151, 257, 131071, 19, 524287, 41, 337, 683, 47, 178481, 241, 601, 1801, 2731, 262657, 29, 113, 233, 1103, 2089, 331, 2147483647, 65537, 599479, 43691, 71, 122921, 37, 109, 223, 616318177, 174763, 79 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Or, primitive prime divisors of the Mersenne numbers 2^n-1 (see A000225) in their order of occurrence. Of course the Mersenne primes 2^p-1 (cf. A000043) appear in this sequence. If all odd positive numbers, not just the odd primes, are sorted in this way, the result is A059912. - Jeppe Stig Nielsen, Feb 13 2020 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..4275 G. Everest et al., Primes generated by recurrence sequences, Amer. Math. Monthly, 114 (No. 5, 2007), 417-431. Jeppe Stig Nielsen, A108974 arranged as an irregular array. K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math., 3 (1892), 265-284. EXAMPLE The order of 2 modulo 3 is 2 and the order of 2 modulo 7 is 3. So 3 comes before 7. MATHEMATICA a = 1; DeleteDuplicates[Flatten[#[[All, 1]] & /@ FactorInteger[Table[a = 2 a + 1, {i, 1, 30}]]]] (* Horst H. Manninger, Mar 20 2021 *) PROG (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 CROSSREFS Cf. A000043, A000225, A001348, A014664, A059912, A086251. Sequence in context: A212953 A161818 A161509 * A106853 A083778 A107785 Adjacent sequences:  A108971 A108972 A108973 * A108975 A108976 A108977 KEYWORD nonn AUTHOR Douglas Stones (dssto1(AT)student.monash.edu.au), Jul 27 2005 EXTENSIONS More terms from Martin Fuller, Sep 25 2006 STATUS approved

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Last modified August 2 04:47 EDT 2021. Contains 346409 sequences. (Running on oeis4.)