A151821 Powers of 2, omitting 2 itself.

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

Offset: 1

Author

N. J. A. Sloane, Jul 08 2009

Keywords

• nonn
• easy

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 n-Keller graph. - Eric W. Weisstein, Nov 17 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Paul Barry, On a Central Transform of Integer Sequences, arXiv:2004.04577 [math.CO], 2020.
• Eric Weisstein's World of Mathematics, Chromatic Number
• Eric Weisstein's World of Mathematics, Keller Graph
• Index entries for linear recurrences with constant coefficients, signature (2).

Crossrefs

Cf. A000079, A007483, A018252, A020707, A046055, A055744, A063759, A095121, A175655.

Partial sums are given by 2*A000225(n)-1, which is not the same as A000918.

Programs

Haskell

a151821 n = a151821_list !! (n-1)
a151821_list = x : xs where (x : _ : xs) = a000079_list
-- Reinhard Zumkeller, Dec 16 2013

Magma

[1] cat [2^n: n in [2..35]]; // Vincenzo Librandi, Jul 21 2013

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 *)

PARI

a(n)=if(n>1,2^n,1) \\ Charles R Greathouse IV, Dec 08 2015

PARI

Vec(x*(1+2*x)/(1-2*x) + O(x^100)) \\ Altug Alkan, Dec 09 2015

Python

def A151821(n): return 1<1 else 1 # Chai Wah Wu, Jun 10 2025

Formula

G.f.: x*(1+2*x)/(1-2*x). - Philippe Deléham, Sep 17 2009

a(1) = 1 and a(n) = 3 + Sum_{k=1..n-1} a(k) for n>=2. - Joerg Arndt, Aug 15 2012

E.g.f.: exp(2*x) - x - 1. - Stefano Spezia, Jan 31 2023