A316661 a(n) = ceiling(sqrt((2*n)^n)).

1, 2, 4, 15, 64, 317, 1728, 10268, 65536, 445376, 3200000, 24172677, 191102976, 1575167570, 13492928512, 119786923327, 1099511627776, 10412878353557, 101559956668416, 1018460448140641, 10485760000000000, 110692335104026964, 1196683881290399744

Offset: 0

Author

Greg Huber, Jul 09 2018

Keywords

• nonn
• easy

Comments

a(0)=1 relies on the algebraic identity 0^0 = 1 (à la Knuth).

Links

• D. E. Knuth, Two Notes on Notation, The American Mathematical Monthly, 99 (1992), 403-422.

Crossrefs

Cf. A242764.

Programs

Magma

[Ceiling(Sqrt((2*n)^n)): n in [0..25]]; // Vincenzo Librandi, Jul 10 2018

Mathematica

Join[{1}, Table[Ceiling[Sqrt[(2 n)^n]], {n, 30}]] (* Vincenzo Librandi, Jul 10 2018 *)

PARI

a(n) = ceil(sqrt((2*n)^n)); \\ Michel Marcus, Jul 10 2018

Python

from math import isqrt
def A316661(n): return 1+isqrt((n<<1)**n-1) # Chai Wah Wu, Jul 29 2022