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 A156638 #61 Nov 23 2024 05:46:31
%S A156638 4,5,13,14,22,23,31,32,40,41,49,50,58,59,67,68,76,77,85,86,94,95,103,
%T A156638 104,112,113,121,122,130,131,139,140,148,149,157,158,166,167,175,176,
%U A156638 184,185,193,194,202,203,211,212,220,221,229,230,238,239,247,248,256
%N A156638 Numbers k such that k^2 + 2 == 0 (mod 9).
%C A156638 From _Artur Jasinski_, Apr 30 2010: (Start)
%C A156638 Numbers congruent to 4 or 5 mod 9.
%C A156638 Numbers which are not the sum of 3 cubes.
%C A156638 Complement to A060464. (End)
%C A156638 Numbers k such that A010888(k^2) = 7. - _V.J. Pohjola_, Aug 18 2012
%D A156638 Henri Cohen, Number Theory Volume I: Tools and Diophantine Equations. Springer Verlag (2007) p. 380. - _Artur Jasinski_, Apr 30 2010
%H A156638 Vincenzo Librandi, <a href="/A156638/b156638.txt">Table of n, a(n) for n = 1..1000</a>
%H A156638 Andrew Sutherland, <a href="https://drive.google.com/file/d/1qzD__dviONTqHQH7DBFmsQ0MdCa7ePRg/view">Sums of three cubes</a>, Slides of a talk given May 07 2020 on the Number Theory Web.
%H A156638 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A156638 For n > 2, a(n) = a(n-2) + 9.
%F A156638 G.f.: x*(4*x^2 + x + 4)/(x^3 - x^2 - x + 1). - _Alexander R. Povolotsky_, Feb 15 2009
%F A156638 From _R. J. Mathar_, Feb 19 2009: (Start)
%F A156638 a(n) = a(n-1) + a(n-2) - a(n-3), n>3.
%F A156638 a(n) = 9*n/2 - 9/4 - 7*(-1)^n/4.
%F A156638 G.f.: x*(4 + x + 4*x^2)/((1 + x)*(1 - x)^2). (End)
%F A156638 a(n) = -a(-n+1). - _Bruno Berselli_, Jan 08 2012
%F A156638 E.g.f.: 4 + ((18*x - 9)*exp(x) - 7*exp(-x))/4. - _David Lovler_, Aug 21 2022
%F A156638 Sum_{n>=1} (-1)^(n+1)/a(n) = tan(Pi/18)*Pi/9. - _Amiram Eldar_, Sep 26 2022
%F A156638 From _Amiram Eldar_, Nov 22 2024: (Start)
%F A156638 Product_{n>=1} (1 - (-1)^n/a(n)) = 1.
%F A156638 Product_{n>=1} (1 + (-1)^n/a(n)) = 2*cos(Pi/9) - 1 (= A332437 - 1). (End)
%p A156638 A156638:=n->9*n/2 - 9/4 - 7*(-1)^n/4: seq(A156638(n), n=1..80); # _Wesley Ivan Hurt_, Aug 16 2015
%t A156638 LinearRecurrence[{1, 1, -1}, {4, 5, 13}, 50] (* _Vincenzo Librandi_, Mar 01 2012 *)
%t A156638 Flatten[Table[9n - {5, 4}, {n, 30}]] (* _Alonso del Arte_, Aug 09 2015 *)
%t A156638 Select[Range[300],PowerMod[#,2,9]==7&] (* _Harvey P. Dale_, Jan 31 2023 *)
%o A156638 (Magma) [9*n/2 - 9/4 - 7*(-1)^n/4 : n in [1..80]]; // _Wesley Ivan Hurt_, Aug 16 2015
%o A156638 (PARI) a(n) = (18*n - 9 - 7*(-1)^n)/4 \\ _David Lovler_, Aug 21 2022
%Y A156638 Cf. A060464, A010888, A332437, A334521, A334522.
%K A156638 nonn,easy
%O A156638 1,1
%A A156638 _Vincenzo Librandi_, Feb 12 2009