The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A307611 An Ackermann-like function arising from a puzzle by Hans Zantema. 1
 1, 2, 4, 8, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). The derivation and proof of the general formula involving a sequence of up-arrows is by Richard Stong, Dan Velleman, and Stan Wagon. The next term is too large to include (2^65537, it has 19729 digits). REFERENCES Dan Velleman and Stan Wagon, Bicycle or Unicycle?, MAA Press, to appear. LINKS Wikipedia, Knuth's up-arrow notation FORMULA Let f_n(x) = 2↑↑...↑x, with n Knuth up-arrows, so f_0(x) = 2x,   f_1(x) = 2^x, f_2(x) = 2↑↑x = 2^2^...^2 with x copies of 2, etc. Let   F_n be the composition of f_0, f_1,...,f_n. Then a(n) = F_(n-2)(1). EXAMPLE a(6) = f_0(f_1(f_2(f_3(f_4(1))))) = f_0(f_1(f_2(f_3(2))))       = f_0(f_1(f_2(4))) = f_0(f_1(65536)) = f_0(2^65536) = 2^65537. MATHEMATICA f[n_][x_] := If[n == 0, 2x, Nest[f[n-1], 1, x]] F[n_] := Composition @@ (f /@ Range[0, n]) a[n_] := If[n <= 1, n, F[n-2][1]] CROSSREFS Cf. A281701. Sequence in context: A018355 A100083 A151406 * A053147 A128055 A061285 Adjacent sequences:  A307608 A307609 A307610 * A307612 A307613 A307614 KEYWORD nonn AUTHOR Stan Wagon, Apr 18 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 16 00:05 EST 2021. Contains 340195 sequences. (Running on oeis4.)