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a(n) = floor(log(log(n^n^n))) (or 0 if not finite).
0

%I #9 Jan 01 2024 13:36:56

%S 0,1,3,5,8,11,14,17,20,23,27,30,34,37,41,45,49,53,57,61,65,69,73,77,

%T 81,85,90,94,98,103,107,112,116,121,125,130,134,139,144,148,153,158,

%U 163,167,172,177,182,187,192,196,201,206,211,216,221,226,231,236,241,247

%N a(n) = floor(log(log(n^n^n))) (or 0 if not finite).

%F a(n) = floor(n*log(n) + log(log(n))).

%e 3^3^3 = 3^27 = 7625597484987. Log(log(7625597484987)) = 3.38..., so a(3)= 3.

%t Table[ Floor[ n * Log[n] + Log[ Log[n]]], {n, 2, 60}]

%Y Cf. A002488, A000312, A050504.

%K nonn

%O 1,3

%A _Neil Fernandez_, Nov 20 2002

%E Edited by _Robert G. Wilson v_, Nov 22 2002