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 A047341 #50 Nov 22 2024 06:27:23
%S A047341 3,4,10,11,17,18,24,25,31,32,38,39,45,46,52,53,59,60,66,67,73,74,80,
%T A047341 81,87,88,94,95,101,102,108,109,115,116,122,123,129,130,136,137,143,
%U A047341 144,150,151,157,158,164,165,171
%N A047341 Numbers that are congruent to {3, 4} mod 7.
%C A047341 Numbers m such that m^2 == 2 (mod 7). - _Vincenzo Librandi_, Aug 05 2010
%C A047341 Numbers k such that A056107(k)/7 is an integer. - _Bruno Berselli_, Feb 14 2017
%H A047341 David Lovler, <a href="/A047341/b047341.txt">Table of n, a(n) for n = 1..1000</a>
%H A047341 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047341 a(n)^2 = 7*A056834(a(n)) + 2. - _Bruno Berselli_, Nov 28 2010
%F A047341 G.f.: x*(3 + x + 3*x^2)/((1 + x)*(1 - x)^2). - _R. J. Mathar_, Oct 08 2011
%F A047341 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*tan(Pi/14)/7. - _Amiram Eldar_, Dec 12 2021
%F A047341 E.g.f.: 3 + ((14*x - 7)*exp(x) - 5*exp(-x))/4. - _David Lovler_, Sep 01 2022
%F A047341 From _Amiram Eldar_, Nov 22 2024: (Start)
%F A047341 Product_{n>=1} (1 - (-1)^n/a(n)) = 1.
%F A047341 Product_{n>=1} (1 + (-1)^n/a(n)) = 2*cos(Pi/7) - 1 (A160389 - 1). (End)
%t A047341 LinearRecurrence[{1, 1, -1}, {3, 4, 10}, 50] (* _Amiram Eldar_, Dec 12 2021 *)
%o A047341 (PARI) a(n) = (14*n-5*(-1)^n-7)/4 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y A047341 Cf. A056107, A056834, A160389.
%K A047341 nonn,easy
%O A047341 1,1
%A A047341 _N. J. A. Sloane_