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 A083575 #41 Aug 04 2024 02:58:33
%S A083575 6,11,21,41,81,161,321,641,1281,2561,5121,10241,20481,40961,81921,
%T A083575 163841,327681,655361,1310721,2621441,5242881,10485761,20971521,
%U A083575 41943041,83886081,167772161,335544321,671088641,1342177281,2684354561,5368709121,10737418241
%N A083575 a(0) = 6; for n>0, a(n) = 2*a(n-1) - 1.
%C A083575 The primes in this sequence are listed in A050526. - _M. F. Hasler_, Oct 30 2010
%C A083575 An Engel expansion of 2/5 to the base 2 as defined in A181565, with the associated series expansion 2/5 = 2/6 + 2^2/(6*11) + 2^3/(6*11*21) + 2^4/(6*11*21*41) + ... . - _Peter Bala_, Oct 29 2013
%H A083575 Vincenzo Librandi, <a href="/A083575/b083575.txt">Table of n, a(n) for n = 0..1000</a>
%H A083575 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A083575 a(n) = 5*2^n + 1. - _M. F. Hasler_, Oct 30 2010
%F A083575 a(n) = 3*a(n-1) - 2*a(n-2), n>1. - _Vincenzo Librandi_, Nov 03 2011
%F A083575 G.f.: (6-7*x) / ((1-x)*(1-2*x)). - _Colin Barker_, Sep 20 2016
%F A083575 E.g.f.: exp(x)*(1 + 5*exp(x)). - _Stefano Spezia_, Oct 08 2022
%F A083575 Product_{n>=0} (1 + 1/a(n)) = 7/5. - _Amiram Eldar_, Aug 04 2024
%t A083575 NestList[2#-1&,6,40] (* _Harvey P. Dale_, Jun 23 2017 *)
%o A083575 (PARI) a(n)=5<<n+1 \\ _M. F. Hasler_, Oct 30 2010
%o A083575 (Magma) [5*2^n+1 : n in [0..30]]; // _Vincenzo Librandi_, Nov 03 2011
%o A083575 (PARI) Vec((6-7*x)/((1-x)*(1-2*x)) + O(x^40)) \\ _Colin Barker_, Sep 20 2016
%Y A083575 Cf. A020737, A050526, A083683, A083686, A083705, A168596, A181565, A195744.
%K A083575 nonn,easy
%O A083575 0,1
%A A083575 _N. J. A. Sloane_, Jun 15 2003