A353343 Smallest k such that k-th derivative of f_n(x) at x=1 is nonpositive, where f_{-1}(x)=0 and f_n(x)=x^(f_{n-1}(x)).

0, 1, 2, 7, 33, 329

Offset

-1,3

Comments

f_{-1}(x)=0,

f_0(x)=1,

f_1(x)=x,

f_n(x)=x^(x^(x^...)) is a power tower with n levels.

Links

Table of n, a(n) for n=-1..4.

Eric Weisstein's World of Mathematics, Power Tower.

Mathematica

Table[Length[NestWhileList[Expand[D[#, x]] &, Nest[x^# &, 0, n + 1], (# /. x -> 1) > 0 &]] - 1, {n, -1, 3}]

Crossrefs

Cf. A005727, A179230, A179405, A179505, A277537.

Sequence in context: A241767 A222940 A227120 * A376055 A387525 A023053

Adjacent sequences: A353340 A353341 A353342 * A353344 A353345 A353346

Keyword

nonn,hard,more

Author

Vladimir Reshetnikov, May 06 2022

Status

approved