login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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
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
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: A152730 A361700 A090027 * A290008 A377406 A121616
KEYWORD
nonn,easy
AUTHOR
Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009
STATUS
approved