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 A332203 #16 Oct 14 2024 20:29:47
%S A332203 2,3,9,129,32769,2147483649,9223372036854775809,
%T A332203 170141183460469231731687303715884105729,
%U A332203 57896044618658097711785492504343953926634992332820282019728792003956564819969
%N A332203 a(n) = 2^(2^n-1) + 1.
%C A332203 All terms > 2 are divisible by 3. Moreover, the exponent of the highest power of 3 dividing a(n) behaves like a mixture of 2- and 3-adic ruler function, after the initial 0: (1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 4, ...) = A332202.
%F A332203 a(n) = A000051(A000225(n)) = 2^A000225(n) + 1 = A077585(n) + 2.
%t A332203 a[n_] := 2^(2^n-1) + 1; Array[a,9,0] (* _Stefano Spezia_, Oct 14 2024 *)
%o A332203 (PARI) apply( {A332203(n)=1<<(1<<n-1)+1}, [0..9])
%Y A332203 Cf. A077585 (Double Mersenne numbers: same with -1), A000225 (Mersenne numbers 2^n-1).
%K A332203 nonn
%O A332203 0,1
%A A332203 _M. F. Hasler_, Mar 05 2020