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A164784 a(n) = 6^n-5. 3
1, 31, 211, 1291, 7771, 46651, 279931, 1679611, 10077691, 60466171, 362797051, 2176782331, 13060694011, 78364164091, 470184984571, 2821109907451, 16926659444731, 101559956668411, 609359740010491, 3656158440062971 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

REFERENCES

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

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. 153-157.

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(n-1)+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^n-5: 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

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Last modified December 3 09:03 EST 2022. Contains 358515 sequences. (Running on oeis4.)