This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164783 #41 Jan 05 2025 19:51:39
%S A164783 1,43,337,2395,16801,117643,823537,5764795,40353601,282475243,
%T A164783 1977326737,13841287195,96889010401,678223072843,4747561509937,
%U A164783 33232930569595,232630513987201,1628413597910443,11398895185373137
%N A164783 a(n) = 7^n-6.
%C A164783 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.
%D A164783 Daniel Minoli, Sufficient Forms For Generalized Perfect Numbers, Ann. Fac. Sciences, Univ. Nation. Zaire, Section Mathem. Vol. 4, No. 2, Dec 1978, pp. 277-302.
%D A164783 Daniel Minoli, New Results For Hyperperfect Numbers, Abstracts American Math. Soc., October 1980, Issue 6, Vol. 1, pp. 561.
%D A164783 Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (p.114-134)
%H A164783 Vincenzo Librandi, <a href="/A164783/b164783.txt">Table of n, a(n) for n = 1..1000</a>
%H A164783 Daniel Minoli, <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0559206-9">Issues In Non-Linear Hyperperfect Numbers</a>, Mathematics of Computation, Vol. 34, No. 150, April 1980, pp. 639-645.
%H A164783 D. Minoli, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/19-1/minoli.pdf">Structural Issues For Hyperperfect Numbers</a>, Fibonacci Quarterly, Feb. 1981, Vol. 19, No. 1, pp. 6-14.
%H A164783 D. Minoli and Robert Bear, <a href="http://www.pme-math.org/journal/issues/PMEJ.Vol.6.No.3.pdf">Hyperperfect Numbers</a>, Pi Mu Epsilon Journal, Fall 1975, pp. 153-157.
%H A164783 Daniel Minoli and W. Nakamine, <a href="http://dx.doi.org/10.1109/ICASSP.1980.1170906">Mersenne Numbers Rooted On 3 For Number Theoretic Transforms</a>, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing.
%H A164783 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A164783 a(n) = 7*a(n-1)+36 with n>1, a(1)=1. - _Vincenzo Librandi_, Nov 30 2010
%F A164783 G.f.: x*(1+35*x)/((1-x)*(1-7*x)). - _Colin Barker_, Mar 08 2012
%F A164783 a(n) = 8*a(n-1) - 7*a(n-2) for n>2, a(1)=1, a(2)=43. - _Vincenzo Librandi_, Feb 06 2013
%F A164783 a(n) = A000420(n) - 6 for n>0. - _Michel Marcus_, Aug 31 2013
%t A164783 CoefficientList[Series[(1 + 35 x)/((1-x) (1-7 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 06 2013 *)
%t A164783 NestList[7 # + 36 & , 1, 18] (* _Bruno Berselli_, Feb 06 2013 *)
%t A164783 LinearRecurrence[{8,-7},{1,43},30] (* _Harvey P. Dale_, Nov 27 2014 *)
%o A164783 (Magma) [7^n-6: n in [1..30]]; // _Vincenzo Librandi_, Feb 06 2013
%o A164783 (PARI) a(n)=7^n-6 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A164783 Cf. A000420.
%Y A164783 Cf. A014232, A014224, A135535, A059266.
%K A164783 nonn,easy
%O A164783 1,2
%A A164783 Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009
%E A164783 More terms a(8)-a(19) from _Vincenzo Librandi_, Oct 29 2009