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a(0) = 0; for n >= 0, a(n+1) = 2^a(n) + 1.
2

%I #15 Mar 26 2023 12:45:25

%S 0,2,5,33,8589934593

%N a(0) = 0; for n >= 0, a(n+1) = 2^a(n) + 1.

%F a(n+1) = A000051(a(n)). - _Reinhard Zumkeller_, Jan 31 2015

%t RecurrenceTable[{a[0]==0, a[n]==2^a[n-1] + 1}, a, {n, 5}] (* _Vincenzo Librandi_, Feb 01 2015 *)

%t NestList[2^#+1&,0,4] (* _Harvey P. Dale_, Mar 26 2023 *)

%o (Haskell)

%o a254429 n = a254429_list !! n

%o a254429_list = iterate ((+ 1) . (2 ^)) 0

%o -- _Reinhard Zumkeller_, Jan 31 2015

%o (Magma) [n le 2 select 2*(n-1) else 2^Self(n-1)+1: n in [1..5]]; // _Vincenzo Librandi_, Feb 01 2015

%Y Cf. A007013, A254411.

%Y Cf. A000051.

%K nonn

%O 0,2

%A _Max Alekseyev_, Jan 30 2015