A332203 a(n) = 2^(2^n-1) + 1.

2, 3, 9, 129, 32769, 2147483649, 9223372036854775809, 170141183460469231731687303715884105729, 57896044618658097711785492504343953926634992332820282019728792003956564819969

Offset: 0

Author

M. F. Hasler, Mar 05 2020

Keywords

• nonn

Comments

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.

Crossrefs

Cf. A077585 (Double Mersenne numbers: same with -1), A000225 (Mersenne numbers 2^n-1).

Programs

Mathematica

a[n_] := 2^(2^n-1) + 1; Array[a,9,0] (* Stefano Spezia, Oct 14 2024 *)

PARI

apply( {A332203(n)=1<<(1<
				

Formula

a(n) = A000051(A000225(n)) = 2^A000225(n) + 1 = A077585(n) + 2.