A361669 a(n) = floor of sinh(sinh(sinh(...(1)...))) with n iterations.

1, 1, 1, 2, 3, 22, 3355531547

Offset: 0

Author

Sylvia Zevi Abrams, Mar 20 2023

Keywords

• nonn
• easy

Comments

a(7) = ~2.67*10^1457288834.

sinh(x) = (e^x - e^-x)/2 is dominated by e^x as x tends to infinity, meaning that the sequence grows tetrationally.

Examples

			a(0) = 1,
a(1) = floor(sinh(1)) = floor(1.175...) = 1,
a(2) = floor(sinh(sinh(1))) = floor(1.465...) = 1,
a(3) = floor(sinh(sinh(sinh(1)))) = floor(2.048...) = 2,
a(4) = floor(sinh(sinh(sinh(sinh(1))))) = floor(3.812...) = 3,
a(5) = floor(sinh(sinh(sinh(sinh(sinh(1)))))) = floor(22.627...) = 22,
a(6) = floor(sinh(sinh(sinh(sinh(sinh(sinh(1))))))) = 3355531547.
		

Links

• Eric Weisstein's World of Mathematics, Hyperbolic Sine.

Crossrefs

Cf. A000471, A073742.

Programs

Maple

a:= n-> floor(evalf((sinh@@n)(1), 45)):
seq(a(n), n=0..6);  # Alois P. Heinz, Mar 20 2023

Mathematica

Table[Floor[Nest[Sinh[n],1,n]],{n,0,7}]