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%I M2352 N0929 #61 Jul 19 2021 21:19:13
%S 1,3,4,8,65536
%N a(n) = H_n(2,n) where H_n is the n-th hyperoperator.
%C Originally named: An Ackermann function.
%C For hyperoperator definitions and links, see A054871.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H W. Ackermann, <a href="http://eretrandre.org/rb/files/Ackermann1928_126.pdf">Zum Hilbertschen Aufbau der reellen Zahlen</a>, Math. Ann. 99 (1928), 118-133.
%H R. C. Buck, <a href="http://www.jstor.org/stable/2312881">Mathematical induction and recursive definitions</a>, Amer. Math. Monthly, 70 (1963), 128-135.
%H Y. Sundblad, <a href="http://dx.doi.org/10.1007/BF01935330">The Ackermann function. A theoretical, computational and formula manipulative study</a>, Nordisk Tidskr. Informationsbehandling (BIT) 11 (1971), 107-119.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AckermannFunction.html">Ackermann Function.</a>
%H R. G. Wilson v, <a href="/A006987/a006987.pdf">Letter to N. J. A. Sloane, Jan. 1989</a>
%H R. G. Wilson v, <a href="/A001695/a001695.pdf">Letters to BYTE Magazine (1988) and N. J. A. Sloane (1994)</a>
%H <a href="/index/Ab#Ackermann">Index entries for sequences related to Ackermann function</a>
%F Alternative formula:
%F With f(x,y)=
%F {y+1 if x=0
%F {0 if x=2, y=0
%F {1 if x>2, y=0
%F {2 if x=1, y=0
%F {f(x-1,f(x,y-1)) otherwise
%F a(n)= f(n,n);
%e a(0) = H_0(2,0) = 0+1 = 1;
%e a(1) = H_1(2,1) = 2+1 = 3;
%e a(2) = H_2(2,2) = 2*2 = 4;
%e a(3) = H_3(2,3) = 2^3 = 8;
%e a(4) = H_4(2,4) = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536;
%e a(5) = H_5(2,5) = 2^^^5 = 2^^2^^2^^2^^2 = 2^^2^^2^^4 = 2^^2^^65536 = ....
%Y Cf. A014221, A046859, A054871.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_, following a suggestion from _Robert G. Wilson v_, Aug 31 1994
%E Example, formula and Hyperoperator notation by _Natan Arie Consigli_ with _Danny Rorabaugh_'s help, Oct 25 2015
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