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 A307611 #9 Apr 19 2019 10:33:07 %S A307611 1,2,4,8,32 %N A307611 An Ackermann-like function arising from a puzzle by Hans Zantema. %C A307611 a(n) is the largest number of coins obtainable by making repeated moves in this puzzle: Start with empty boxes B(i), i=1..n, and place one coin in B(1). One can iterate moves of two types: (1) remove a coin from a nonempty B(i) (i <= n-1) and place two coins in B(i+1); (2) remove a coin from a nonempty B(i) (i <= n-2) and switch the contents of B(i+1) and B(i+2). %C A307611 The derivation and proof of the general formula involving a sequence of up-arrows is by Richard Stong, Dan Velleman, and Stan Wagon. %C A307611 The next term is too large to include (2^65537, it has 19729 digits). %D A307611 Dan Velleman and Stan Wagon, Bicycle or Unicycle?, MAA Press, to appear. %H A307611 Wikipedia, <a href="https://en.wikipedia.org/wiki/Knuth's_up-arrow_notation">Knuth's up-arrow notation</a> %F A307611 Let f_n(x) = 2↑↑...↑x, with n Knuth up-arrows, so f_0(x) = 2x, %F A307611 f_1(x) = 2^x, f_2(x) = 2↑↑x = 2^2^...^2 with x copies of 2, etc. Let %F A307611 F_n be the composition of f_0, f_1,...,f_n. Then a(n) = F_(n-2)(1). %e A307611 a(6) = f_0(f_1(f_2(f_3(f_4(1))))) = f_0(f_1(f_2(f_3(2)))) %e A307611 = f_0(f_1(f_2(4))) = f_0(f_1(65536)) = f_0(2^65536) = 2^65537. %t A307611 f[n_][x_] := If[n == 0, 2x, Nest[f[n-1], 1, x]] %t A307611 F[n_] := Composition @@ (f /@ Range[0, n]) %t A307611 a[n_] := If[n <= 1, n, F[n-2][1]] %Y A307611 Cf. A281701. %K A307611 nonn %O A307611 1,2 %A A307611 _Stan Wagon_, Apr 18 2019