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 A103127 #33 Dec 27 2023 08:54:58 %S A103127 1,3,5,15,17,19,21,31,33,35,37,47,49,51,53,63,65,67,69,79,81,83,85,95, %T A103127 97,99,101,111,113,115,117,127,129,131,133,143,145,147,149,159,161, %U A103127 163,165,175,177,179,181,191,193,195,197,207,209,211,213,223,225,227,229,239,241 %N A103127 Numbers congruent to {-1, 1, 3, 5} mod 16. %C A103127 Agrees with A103192 for the first 511 terms, but then diverges (see comment in A103192). - _Bruno Berselli_, Dec 01 2016 %H A103127 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>]. %H A103127 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1). %H A103127 <a href="/index/Se#sequences_which_agree_for_a_long_time">Index entries for sequences which agree for a long time but are different</a> %F A103127 a(n) = 2*A047527(n) + 1. %F A103127 From _R. J. Mathar_, Aug 30 2008: (Start) %F A103127 O.g.f.: x*(1 + 2*x + 2*x^2 + 10*x^3 + x^4)/((1 - x)^2*(1 + x)*(1 + x^2)). %F A103127 a(n) = a(n-4) + 16. (End) %F A103127 a(n) = 2*A047476(n+1) - 1. - _Philippe Deléham_, Dec 01 2016 %t A103127 Select[Range[300],MemberQ[{1,3,5,15},Mod[#,16]]&] (* _Harvey P. Dale_, Aug 10 2019 *) %o A103127 (Haskell) %o A103127 a103127 n = a103127_list !! (n-1) %o A103127 a103127_list = [x | x <- [1..], x `mod` 16 `elem` [1,3,5,15]] %o A103127 -- _Reinhard Zumkeller_, Jul 21 2012 %Y A103127 Cf. A047527, A103192. %K A103127 nonn,easy %O A103127 1,2 %A A103127 _N. J. A. Sloane_, Mar 25 2005