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 A090772 #51 Nov 23 2024 05:44:19
%S A090772 2,8,12,18,22,28,32,38,42,48,52,58,62,68,72,78,82,88,92,98,102,108,
%T A090772 112,118,122,128,132,138,142,148,152,158,162,168,172,178,182,188,192,
%U A090772 198,202,208,212,218,222,228,232,238,242,248,252,258,262,268,272,278,282
%N A090772 Numbers that are congruent to {2, 8} mod 10.
%C A090772 Their square ends in the digit 4. - _Kausthub Gudipati_, Sep 08 2011
%C A090772 10*a(n) = 20, 80, 120, 180, 220, ... are the only numbers written in French ending in "vingt(s)". - _Paul Curtz_, Aug 02 2018
%H A090772 G. C. Greubel, <a href="/A090772/b090772.txt">Table of n, a(n) for n = 1..5000</a>
%H A090772 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A090772 a(n) = 2 * A047209(n).
%F A090772 a(n) = 10*n - a(n-1) - 10 (with a(1)=2). - _Vincenzo Librandi_, Nov 16 2010
%F A090772 G.f.: 2*x*(1+3*x+x^2)/((1+x)*(1-x)^2). - _Bruno Berselli_, Sep 08 2011
%F A090772 a(1) = 2. For n > 1, a(n) = a(n-1) + A226294(n). - _Felix Fröhlich_, Aug 02 2018
%F A090772 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1+2/sqrt(5))*Pi/10. - _Amiram Eldar_, Dec 28 2021
%F A090772 E.g.f.: 2 + ((10*x - 5)*exp(x) + exp(-x))/2. - _David Lovler_, Sep 03 2022
%F A090772 From _Amiram Eldar_, Nov 23 2024: (Start)
%F A090772 Product_{n>=1} (1 - (-1)^n/a(n)) = tan(3*Pi/10) (A019952).
%F A090772 Product_{n>=1} (1 + (-1)^n/a(n)) = cosec(2*Pi/5)/2 (= A179290 / 2). (End)
%t A090772 Union@ Flatten@ Outer[Plus, {2, 8}, 10 Range[0, 28]] (* or *)
%t A090772 CoefficientList[Series[2 (1 + 3x + x^2)/((1 + x) (1 - x)^2), {x, 0, 57}], x] (* _Michael De Vlieger_, Aug 02 2018 *)
%t A090772 LinearRecurrence[{1, 1, -1}, {2, 8, 12}, 61] (* _Robert G. Wilson v_, Aug 08 2018 *)
%o A090772 (PARI) is(n) = #setintersect([2, 8], [n%10]) > 0 \\ _Felix Fröhlich_, Aug 02 2018
%o A090772 (PARI) Vec(2*x*(1+3*x+x^2)/((1+x)*(1-x)^2) + O(x^60)) \\ _Felix Fröhlich_, Aug 02 2018
%o A090772 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(2*x*(1+3*x+x^2)/((1+x)*(1-x)^2))); // _G. C. Greubel_, Aug 08 2018
%Y A090772 Cf. A019952, A047209, A090298, A179290, A226294, A317633.
%K A090772 nonn,easy
%O A090772 1,1
%A A090772 _Giovanni Teofilatto_, Feb 07 2004
%E A090772 Edited and extended by _Ray Chandler_, Feb 10 2004