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A108974
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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.
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6
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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The order of 2 modulo 3 is 2 and the order of 2 modulo 7 is 3. So 3 comes before 7.
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MATHEMATICA
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a = 1; DeleteDuplicates[Flatten[#[[All, 1]] & /@ FactorInteger[Table[a = 2 a + 1, {i, 1, 30}]]]] (* Horst H. Manninger, Mar 20 2021 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Douglas Stones (dssto1(AT)student.monash.edu.au), Jul 27 2005
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EXTENSIONS
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STATUS
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approved
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