

A151821


Powers of 2, omitting 2 itself.


24



1, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296, 8589934592
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OFFSET

1,2


COMMENTS

Different from A046055.
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
This is a subsequence of A055744, numbers n such that n and phi(n) have same prime factors.  Michel Marcus, Mar 20 2015
INVERTi transform of A007483: (1, 5, 17, 61, 217, 773, ...).  Gary W. Adamson, Aug 06 2016
Nonprimes that are also powers of 2. Intersection of A000079 and A018252.  Omar E. Pol, Jan 27 2017
Also the chromatic number of the nKeller graph.  Eric W. Weisstein, Nov 17 2017


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Chromatic Number
Eric Weisstein's World of Mathematics, Keller Graph


FORMULA

G.f.: x*(1+2*x)/(12*x).  Philippe Deléham, Sep 17 2009
a(1) = 1 and a(n) = 3 + Sum_{k=1..n1} a(k) for n>=2.  Joerg Arndt, Aug 15 2012


MATHEMATICA

CoefficientList[Series[(1 + 2 x)/(1  2 x), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 21 2013
DeleteCases[2^Range[0, 33], p_ /; PrimeQ @ p] (* Michael De Vlieger, Aug 06 2016 *)
Join[{1}, 2^Range[2, 20]] (* Eric W. Weisstein, Nov 17 2017 *)


PROG

(MAGMA) [1] cat [2^n: n in [2..35]]; // Vincenzo Librandi, Jul 21 2013
(Haskell)
a151821 n = a151821_list !! (n1)
a151821_list = x : xs where (x : _ : xs) = a000079_list
 Reinhard Zumkeller, Dec 16 2013
(PARI) a(n)=if(n>1, 2^n, 1) \\ Charles R Greathouse IV, Dec 08 2015
(PARI) Vec(x*(1+2*x)/(12*x) + O(x^100)) \\ Altug Alkan, Dec 09 2015


CROSSREFS

Cf. A000079, A000225, A007483, A063759.
Partial sums are given by 2*A000225(n)1, which is not the same as A000918.
Sequence in context: A046055 A186949 A020707 * A147639 A049934 A089890
Adjacent sequences: A151818 A151819 A151820 * A151822 A151823 A151824


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Jul 08 2009


STATUS

approved



