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%I #33 Dec 27 2023 08:54:58
%S 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 97,99,101,111,113,115,117,127,129,131,133,143,145,147,149,159,161,
%U 163,165,175,177,179,181,191,193,195,197,207,209,211,213,223,225,227,229,239,241
%N Numbers congruent to {-1, 1, 3, 5} mod 16.
%C Agrees with A103192 for the first 511 terms, but then diverges (see comment in A103192). - _Bruno Berselli_, Dec 01 2016
%H 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 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%H <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 a(n) = 2*A047527(n) + 1.
%F From _R. J. Mathar_, Aug 30 2008: (Start)
%F O.g.f.: x*(1 + 2*x + 2*x^2 + 10*x^3 + x^4)/((1 - x)^2*(1 + x)*(1 + x^2)).
%F a(n) = a(n-4) + 16. (End)
%F a(n) = 2*A047476(n+1) - 1. - _Philippe Deléham_, Dec 01 2016
%t Select[Range[300],MemberQ[{1,3,5,15},Mod[#,16]]&] (* _Harvey P. Dale_, Aug 10 2019 *)
%o (Haskell)
%o a103127 n = a103127_list !! (n-1)
%o a103127_list = [x | x <- [1..], x `mod` 16 `elem` [1,3,5,15]]
%o -- _Reinhard Zumkeller_, Jul 21 2012
%Y Cf. A047527, A103192.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Mar 25 2005
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