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%I #70 Jun 25 2023 20:37:12
%S 1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,
%T 48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,
%U 94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132
%N 1 together with positive even numbers.
%C Also number of non-attacking bishops on n X n board. - Koksal Karakus (karakusk(AT)hotmail.com), May 27 2002
%C Engel expansion of e^(1/2) (see A006784 for definition) [when offset by 1]. - _Henry Bottomley_, Dec 18 2000
%C Numbers n such that a 2n-group (i.e., a group of order 2n) has subgroup C_2. - _Lekraj Beedassy_, Oct 14 2004
%C Image of 1/(1-2x) under the mapping g(x)->g(x/(1+x^2)). - _Paul Barry_, Jan 16 2005
%C Position of n in A113322: A113322(a(n-1)) = n for n>0. - _Reinhard Zumkeller_, Oct 26 2005
%C Incrementally largest terms in the continued fraction for e. - Nick Hobson, Jan 11 2007
%C Conjecturally, the differences of two consecutive primes (without repetition). - _Juri-Stepan Gerasimov_, Nov 09 2009
%C Equals (1, 2, 2, 2, ...) convolved with (1, 0, 2, 0, 2, 0, 2, ...). - _Gary W. Adamson_, Mar 03 2010
%C a(n) is the number of 0-dimensional elements (vertices) in an n-cross polytope. - _Patrick J. McNab_, Jul 06 2015
%C Numbers k such that in the symmetric representation of sigma(k) there is no pair bars as its ends (Cf. A237593). - _Omar E. Pol_, Sep 28 2018
%C Also, the coordination sequence of the L-lattice (see A332419). - _Sean A. Irvine_, Jul 29 2020
%H E. Friedman, <a href="https://erich-friedman.github.io/mathmagic/0201.html">Math. Magic</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossPolytope.html">Cross Polytope</a>
%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F G.f.: (1+x^2)/(1-x)^2. - _Paul Barry_, Feb 28 2003
%F Inverse binomial transform of Cullen numbers A002064. a(n)=2n+0^n. - _Paul Barry_, Jun 12 2003
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n-k-1)*(-1)^k*2^(n-2k). - _Paul Barry_, Jan 16 2005
%F Equals binomial transform of [1, 1, 1, -1, 1, -1, 1, ...]. - _Gary W. Adamson_, Jul 15 2008
%F E.g.f.: 1+x*sinh(x) (aerated sequence). - _Paul Barry_, Oct 11 2009
%F a(n) = 0^n + 2*n = A000007(n) + A005843(n). - _Reinhard Zumkeller_, Jan 11 2012
%t Join[{1}, Table[2*n, {n, 200}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 10 2011 *)
%t Select[Range@ 105, PowerMod[#, #, # + 1] == 1 &] (* _Robert G. Wilson v_, Sep 26 2016 *)
%o (Haskell)
%o a004277 n = 2 * n - 1 + signum (1 - n)
%o a004277_list = 1 : [2, 4 ..] -- _Reinhard Zumkeller_, Dec 19 2013
%o (Magma) [1] cat [2*n: n in [1..80]]; // _Vincenzo Librandi_, Jul 11 2015
%Y Cf. A004275, A008486, A030978, A097134.
%Y INVERT transformation yields A098182 without A098182(0). - _R. J. Mathar_, Sep 11 2008
%K easy,nonn
%O 0,2
%A _N. J. A. Sloane_
%E Corrected by _Charles R Greathouse IV_, Mar 18 2010
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