The OEIS is supported by the many generous donors to the OEIS Foundation.

 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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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