



1, 31, 211, 1291, 7771, 46651, 279931, 1679611, 10077691, 60466171, 362797051, 2176782331, 13060694011, 78364164091, 470184984571, 2821109907451, 16926659444731, 101559956668411, 609359740010491, 3656158440062971
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OFFSET

1,2


COMMENTS

Minoli defined the sequences and concepts that follow in the 1980 IEEE paper below:  Sequence m (n,t) = (n^t)  (n1) 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 (nGMN)  If j belonging to the sequence m (n,t) is prime, it is then called a nGeneralized Mersenne Prime (nGMP). Note: m (n,t) = n* m (n,t1) + 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.


REFERENCES

Daniel Minoli, Voice over MPLS, McGrawHill, New York, NY, 2002, ISBN 0071406158 (p.114134)


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Daniel Minoli and Robert Bear, Hyperperfect Numbers, Pi Mu Epsilon Journal, Fall 1975, pp. 153157.
Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing.


FORMULA

a(n) = 6*a(n1)+25 with n>1, a(1)=1.  Vincenzo Librandi, Oct 29 2009
G.f.: x*(1 + 24*x)/(1  7*x + 6*x^2).  Vincenzo Librandi, Feb 06 2013
E.g.f.: 4 + (exp(5*x)  5)*exp(x).  Ilya Gutkovskiy, Jun 11 2016


MATHEMATICA

CoefficientList[Series[(1 + 24 x)/(1  7 x + 6 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)


PROG

(Magma) [6^n5: n in [1..30]]; // Vincenzo Librandi, Feb 06 2013


CROSSREFS

Sequence in context: A022521 A152730 A090027 * A290008 A121616 A284899
Adjacent sequences: A164781 A164782 A164783 * A164785 A164786 A164787


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



