This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001695 M2352 N0929 #62 Feb 16 2025 08:32:24
%S A001695 1,3,4,8,65536
%N A001695 a(n) = H_n(2,n) where H_n is the n-th hyperoperator.
%C A001695 Originally named: An Ackermann function.
%C A001695 For hyperoperator definitions and links, see A054871.
%D A001695 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001695 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001695 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 A001695 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 A001695 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 A001695 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AckermannFunction.html">Ackermann Function.</a>
%H A001695 R. G. Wilson v, <a href="/A006987/a006987.pdf">Letter to N. J. A. Sloane, Jan. 1989</a>
%H A001695 R. G. Wilson v, <a href="/A001695/a001695.pdf">Letters to BYTE Magazine (1988) and N. J. A. Sloane (1994)</a>
%H A001695 <a href="/index/Ab#Ackermann">Index entries for sequences related to Ackermann function</a>
%F A001695 Alternative formula:
%F A001695 With f(x,y)=
%F A001695 {y+1 if x=0
%F A001695 {0 if x=2, y=0
%F A001695 {1 if x>2, y=0
%F A001695 {2 if x=1, y=0
%F A001695 {f(x-1,f(x,y-1)) otherwise
%F A001695 a(n)= f(n,n);
%e A001695 a(0) = H_0(2,0) = 0+1 = 1;
%e A001695 a(1) = H_1(2,1) = 2+1 = 3;
%e A001695 a(2) = H_2(2,2) = 2*2 = 4;
%e A001695 a(3) = H_3(2,3) = 2^3 = 8;
%e A001695 a(4) = H_4(2,4) = 2^^4 = 2^2^2^2 = 2^2^4 = 2^16 = 65536;
%e A001695 a(5) = H_5(2,5) = 2^^^5 = 2^^2^^2^^2^^2 = 2^^2^^2^^4 = 2^^2^^65536 = ....
%Y A001695 Cf. A014221, A046859, A054871.
%K A001695 nonn,nice
%O A001695 0,2
%A A001695 _N. J. A. Sloane_, following a suggestion from _Robert G. Wilson v_, Aug 31 1994
%E A001695 Example, formula and Hyperoperator notation by _Natan Arie Consigli_ with _Danny Rorabaugh_'s help, Oct 25 2015