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%I #101 Feb 01 2023 08:19:05
%S 1,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T 131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592
%N Powers of 2, omitting 2 itself.
%C Different from A046055.
%C An elephant sequence, see A175655. For the central square just one A[5] vector, with decimal value 170, leads to this sequence. For the corner squares this vector leads to the companion sequence A095121. - _Johannes W. Meijer_, Aug 15 2010
%C This is a subsequence of A055744, numbers n such that n and phi(n) have same prime factors. - _Michel Marcus_, Mar 20 2015
%C INVERTi transform of A007483: (1, 5, 17, 61, 217, 773, ...). - _Gary W. Adamson_, Aug 06 2016
%C Nonprimes that are also powers of 2. Intersection of A000079 and A018252. - _Omar E. Pol_, Jan 27 2017
%C Also the chromatic number of the n-Keller graph. - _Eric W. Weisstein_, Nov 17 2017
%H Vincenzo Librandi, <a href="/A151821/b151821.txt">Table of n, a(n) for n = 1..1000</a>
%H Paul Barry, <a href="https://arxiv.org/abs/2004.04577">On a Central Transform of Integer Sequences</a>, arXiv:2004.04577 [math.CO], 2020.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticNumber.html">Chromatic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KellerGraph.html">Keller Graph</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F G.f.: x*(1+2*x)/(1-2*x). - _Philippe Deléham_, Sep 17 2009
%F a(1) = 1 and a(n) = 3 + Sum_{k=1..n-1} a(k) for n>=2. - _Joerg Arndt_, Aug 15 2012
%F E.g.f.: exp(2*x) - x - 1. - _Stefano Spezia_, Jan 31 2023
%t CoefficientList[Series[(1 + 2 x)/(1 - 2 x), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 21 2013
%t DeleteCases[2^Range[0, 33], p_ /; PrimeQ @ p] (* _Michael De Vlieger_, Aug 06 2016 *)
%t Join[{1}, 2^Range[2, 20]] (* _Eric W. Weisstein_, Nov 17 2017 *)
%o (Magma) [1] cat [2^n: n in [2..35]]; // _Vincenzo Librandi_, Jul 21 2013
%o (Haskell)
%o a151821 n = a151821_list !! (n-1)
%o a151821_list = x : xs where (x : _ : xs) = a000079_list
%o -- _Reinhard Zumkeller_, Dec 16 2013
%o (PARI) a(n)=if(n>1,2^n,1) \\ _Charles R Greathouse IV_, Dec 08 2015
%o (PARI) Vec(x*(1+2*x)/(1-2*x) + O(x^100)) \\ _Altug Alkan_, Dec 09 2015
%Y Cf. A000079, A007483, A018252, A046055, A055744, A063759, A095121, A175655.
%Y Partial sums are given by 2*A000225(n)-1, which is not the same as A000918.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jul 08 2009
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