1,2

Minoli defined the sequences and concepts that follow in the 1980 IEEE paper below: - Sequence m(n,t) = (n^t) - (n-1) for t=2 to infinity is called a Mersenne Sequence Rooted on n - If n is prime, this sequence is called a Legitimate Mersenne Sequence - Any j belonging to the sequence m(n,t) is called a Generalized Mersenne Number (n-GMN) - If j belonging to the sequence m (n,t) is prime, it is then called a n-Generalized Mersenne Prime (n-GMP). Note: m (n,t) = n* m (n,t-1) + n^2 - 2*n+1. This sequence related to sequences: A014232 and A014224; A135535 and A059266. These numbers play a role in the context of hyperperfect numbers. For additional references, beyond key ones listed below, see A164783.

Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing.

Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (p.114-134)

Daniel Minoli, Robert Bear, Hyperperfect Numbers, PME (Pi Mu Epsilon) Journal, University Oklahoma, Fall 1975, pp. 153-157.

a(n)=8*a(n-1)+49 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]

For n=2, a(2)=8*1+49=57; n=3, a(3)=8*57+49=505; n=4, a(4)=8*505+49=4089 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]

Sequence in context: A097200 A076459 A027143 this_sequence A166392 A084220 A060891

Adjacent sequences: A164783 A164784 A164785 this_sequence A164787 A164788 A164789

nonn

Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009

More terms a(7)-a(19) from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009