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%I #50 Aug 02 2023 07:17:37
%S 3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,
%T 51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,
%U 97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133
%N The odd numbers greater than 1.
%C Last number of the n-th row of the triangle described in A142717.
%C If negated, these are also the values at local minima of the sequence A141620.
%C a(n) is the shortest leg of the n-th Pythagorean triple with consecutive longer leg and hypotenuse. The n-th such triple is given by (2n+1,2n^2+2n, 2n^2+2n+1), so that the longer legs are A046092(n) and the hypotenuses are A099776(n). - _Ant King_, Feb 10 2011
%C Numbers k such that the symmetric representation of sigma(k) has a pair of bars as its ends (cf. A237593). - _Omar E. Pol_, Sep 28 2018
%C Numbers k such that there is a prime knot with k crossings and braid index 2. (IS this true with "prime" removed?) - _Charles R Greathouse IV_, Feb 14 2023
%H Muniru A Asiru, <a href="/A144396/b144396.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1)
%F a(n) = A005408(n+1) = A000290(n+1) - A000290(n).
%F G.f.: x*(3-x)/(1-x)^2. - _Jaume Oliver Lafont_, Aug 30 2009
%F a(n) = A254858(n-1,2). - _Reinhard Zumkeller_, Feb 09 2015
%p seq(n,n=3..200,2); # _Muniru A Asiru_, Sep 28 2018
%t Range[3, 200, 2] (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2012 *)
%o (Haskell)
%o a144396 = (+ 1) . (* 2)
%o a144396_list = [3, 5 ..] -- _Reinhard Zumkeller_, Feb 09 2015
%o (GAP) List([3,5..200],n->n); # _Muniru A Asiru_, Sep 28 2018
%o (PARI) a(n)=2*n+1 \\ _Charles R Greathouse IV_, Feb 14 2023
%Y Complement of A004275 and of A004277.
%Y Cf. A000217, A002378, A005408, A007395, A046092, A099776, A237593, A254858.
%Y Essentially the same as A140139, A130773, A062545, A020735, A005818.
%K nonn,easy,less
%O 1,1
%A _Paul Curtz_, Oct 03 2008
%E Edited by _R. J. Mathar_, May 21 2009
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