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A004002 Benford numbers: a(n) = e^e^...^e (n times) rounded to nearest integer.

%I A004002 M3010 #35 Jul 20 2024 19:46:06
%S A004002 1,3,15,3814279
%N A004002 Benford numbers: a(n) = e^e^...^e (n times) rounded to nearest integer.
%C A004002 The next term, a(4) ~ 2.3315*10^1656520, has 1656521 decimal digits and is therefore too large to be included. [Rephrased by _M. F. Hasler_, May 01 2013]
%C A004002 Named by Turner (1991) after the American electrical engineer and physicist Frank Albert Benford, Jr. (1883-1948). - _Amiram Eldar_, Jun 26 2021
%D A004002 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A004002 C. W. Clenshaw, F. W. J. Olver and P. R. Turner, <a href="https://doi.org/10.1007/BFb0085718">Level-index arithmetic: An introductory survey</a> in: P. R. Turner (ed.), Numerical Analysis and Parallel Processing, Lecture Notes in Mathematics, Vol. 1397, Springer, Berlin, Heidelberg, 1989, pp. 95-168.
%H A004002 Peter R. Turner, Will the "real" real arithmetic please stand up?, Notices Amer. Math. Soc., Vol. 38 (1991), pp. 298-304; <a href="https://www.ams.org/notices/199104/199104FullIssue.pdf">entire issue</a>.
%H A004002 <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a> (The present sequence seems unrelated to Benford's law!)
%F A004002 a(n) = round(e^e^...^e), where e occurs n times, a(0) = 1 (= e^0). - _Melissa O'Neill_, Jul 04 2015
%p A004002 p:= n-> `if`(n=0, 1, exp(1)^p(n-1)):
%p A004002 a:= n-> round(p(n)):
%p A004002 seq(a(n), n=0..3);  # _Alois P. Heinz_, Jul 20 2024
%t A004002 Round[NestList[Power[E, #] &, 1, 3]] (* _Melissa O'Neill_, Jul 04 2015 *)
%Y A004002 Cf. A056072, A225053.
%Y A004002 Cf. A073236. - _Melissa O'Neill_, Jul 04 2015
%K A004002 nonn
%O A004002 0,2
%A A004002 _N. J. A. Sloane_