a(49) - a(78) from _Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), _, Apr 26 2011

OEIS Server: https://oeis.org/edit/global/888

_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Feb 21 2011

OEIS Server: https://oeis.org/edit/global/228

proposed

approved

Number of prime divisors of n (counted with multiplicity) of n such that the primitive irreducible trinomial x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some k with 0 < k < n (A073726).

1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 3, 3, 2, 2, 1, 2, 3, 1, 1, 2, 2, 4, 2, 1, 1, 2, 3, 2, 2, 2, 4, 3, 2, 3, 1, 1, 1, 4, 4, 2, 1, 2, 2, 2, 1, 3, 4, 1, 3, 2, 5, 2, 1, 2, 2, 2, 2, 3, 1, 2, 3, 4, 2, 4, 1, 4, 2, 2, 3, 4, 1, 3, 2, 2, 1, 2, 3

As of Feb 21, 2011, A074744 only is shown through a(11).

nonn,easy,more

a(49) - a(78) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), Apr 26 2011

approved

proposed

proposed

approved

Number of prime divisors of n (counted with multiplicity) of n such that the primitive irreducible trinomial x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some k with 0 < k < n (A073726).

1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 3, 3, 2, 2, 1, 2, 3, 1, 1, 2, 2, 4, 2, 1, 1, 2, 3, 2, 2, 2, 4, 3, 2, 3, 1, 1, 1, 4, 4, 2, 1, 2, 2, 2, 1, 3, 4

T. D. Noe: I added a few more terms, but I'm not sure why this is important.

Jonathan Vos Post: Sorry I've taken so long to reply to meaningful questions from Charles R Greathouse IV, N. J. A. Sloane, and T. D. Noe.  Teaching 7th and 8th grade Algebra to kids who count on their fingers is exhausting, and my use of the web is heavily filtered at school.  Answer: may or may not be important, depending on whether the fine structure I've been playing with in these trinomials works out.  Might be a dead end.  Hunch plus hint of pattern.  I admit that I sometimes put seqs on OEIS which are building blocks for the seqs still in development. If someone adds a useful comment, it accelerates the collaborative discovery.  If nobody cares, I don't mind a "less." Obviously, the quality of my work varies from irritating and error-studded, to fun connection between cutting-edge work in journals or arXiv and existing seqs not mentioned in the formal literature. I am not intentionally making uninteresting seqs.  I applaud N. J. A. Sloane's recent email about adding actual bibliographic material, rather than just making stuff up, as if on a solitary orbit n a vacuum.  That makes at least a fuzzy boundary between genuine collaboratorative scholars and "the usual suspects."

allocated Number of prime divisors of n (counted with multiplicity) of n such that the primitive irreducible trinomial x^n + x^k + 1 is a primitive irreducible polynomial (mod 2) for some Jonathank Voswith Post0 < k < n (A073726).

1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 3, 3, 2, 2, 1, 2, 3, 1, 1, 2, 2, 4

1,3

As of Feb 21, 2011, A074744 only is shown through a(11).

Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, <a href="http://www.cacr.math.uwaterloo.ca/hac/">Handbook of Applied Cryptography</a>, CRC Press, ISBN: 0-8493-8523-7, October 1996, 816 pages, 5th printing, August 2001.

a(n) = bigomega(A073726(n)) = Omega(A073726(n)) = A001222(A073726(n)).

a(48) = 4 because A073726(48) = 100, and Omega(100 = 2^2 * 5^2) = 4.

Cf. A001222, A073726, See A074744 for corresponding values of k.

allocated

nonn,easy,more

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2011

approved

proposed

Charles R Greathouse IV: I'm sold on the value of primitive trinomials x^n + x^k + 1 in GF(2).  But what is the significance of Omega(n)?

N. J. A. Sloane: There is little point in applying Omega to every sequence in the OEIS. Why did you choose this one?

allocated for Jonathan Vos Post

allocated

approved