This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A137781 #20 Sep 08 2022 08:45:33
%S A137781 3,10,40,544,2560,34816,163840,2228224,136314880,671088640,
%T A137781 34896609280,584115552256,2748779069440,37383395344384,
%U A137781 2286984185774080,146366987889541120,720575940379279360,37469948899722526720,627189298506124754944
%N A137781 a(n) = (2^prime(n) + 2^prime(n+1)) / 4.
%C A137781 Note that 4 is 2^prime(1).
%H A137781 G. C. Greubel, <a href="/A137781/b137781.txt">Table of n, a(n) for n = 1..460</a>
%F A137781 From _Wesley Ivan Hurt_, Mar 27 2015: (Start)
%F A137781 a(n) = A137389(n)/4.
%F A137781 a(n) = (A034785(n) + A034785(n+1))/4. (End)
%p A137781 A137781:=n->(2^ithprime(n)+2^ithprime(n+1))/4: seq(A137781(n), n=1..20); # _Wesley Ivan Hurt_, Mar 27 2015
%t A137781 Table[(2^Prime[n] + 2^Prime[n + 1])/4, {n, 20}] (* _Wesley Ivan Hurt_, Mar 27 2015 *)
%t A137781 (2^#[[1]]+2^#[[2]])/4&/@Partition[Prime[Range[20]],2,1] (* _Harvey P. Dale_, Dec 21 2019 *)
%o A137781 (Magma) [(2^NthPrime(n) + 2^NthPrime(n+1)) / 4: n in [1..20]]; // _Vincenzo Librandi_, Mar 28 2015
%o A137781 (PARI) vector(15,n,(2^prime(n)+2^prime(n+1))/4) \\ _Derek Orr_, Mar 29 2015
%Y A137781 Cf. A034785, A137389.
%K A137781 nonn,easy
%O A137781 1,1
%A A137781 _Alexander R. Povolotsky_, Apr 28 2008