A363257 a(n) = floor( ((a(n-1) + 1) / 2)^2 ) + 1 for n >= 1, with a(0) = 0.

0, 1, 2, 3, 5, 10, 31, 257, 16642, 69247363, 1198799355237125, 359279973529237254190922184970, 32270524844792355518177347536627638351478874995525184567711

Offset: 0

Author

Harry Richman, May 23 2023

Keywords

• nonn

Comments

Iterated application of A033638, with a shift.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..16
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)

Crossrefs

Cf. A003095, A006894, A014980, A033638.

Programs

PARI

a(n) = if(n < 1, 0, floor( ((a(n-1) + 1) / 2)^2 ) + 1) \\ Andrew Howroyd, Jan 01 2024

Formula

a(n) = A033638(a(n-1)+1) for n > 0.

log a(n) ~ C * 2^n for some constant C.