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a(n) = ceiling(2^(n+1)/n).
3

%I #15 Sep 08 2022 08:45:00

%S 4,4,6,8,13,22,37,64,114,205,373,683,1261,2341,4370,8192,15421,29128,

%T 55189,104858,199729,381301,729445,1398102,2684355,5162221,9942054,

%U 19173962,37025581,71582789,138547333,268435456,520602097

%N a(n) = ceiling(2^(n+1)/n).

%H Vincenzo Librandi, <a href="/A053639/b053639.txt">Table of n, a(n) for n = 1..1000</a>

%p A053639:=n->ceil(2^(n+1)/n): seq(A053639(n), n=1..40); # _Wesley Ivan Hurt_, Jan 19 2017

%t Table[Ceiling[2^(n+1)/n],{n,1,40}] (* _Vincenzo Librandi_, Dec 19 2011 *)

%o (Magma) [Ceiling(2^(n+1)/n): n in [1..40]]; // _Vincenzo Librandi_, Dec 19 2011

%o (PARI) vector(40, n, ceil(2^(n+1)/n) ) \\ _G. C. Greubel_, May 17 2019

%o (Sage) [ceil(2^(n+1)/n) for n in (1..40)] # _G. C. Greubel_, May 17 2019

%Y Cf. A053637, A053638.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_, Mar 23 2000