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.

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

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 A352011 A083778

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