The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A004231 Ackermann's sequence: n^^n := n^n^n^...^n (with n n's). 7
 1, 1, 4, 7625597484987 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Using Knuth's arrow notation, this is n^^^2 (n-penta-2) or n^^n (n-tetra-n). - Andrew Robbins, Apr 16 2009 Comment from Trevor Green: The fourth term in this sequence has about as many digits - 8.07 * 10^153 - as the *square* of the number of protons in the universe. We could prepend a(0) = 1 (since 0^^0 = 1, that is, the "empty power tower" gives the "empty product"). - Daniel Forgues, May 17 2013 The last 60 decimal digits of a(4) are ...67586985427238232605843019607448189676936860456095261392896. - Daniel Forgues, Jun 25 2016 From Daniel Forgues, Jul 06 2016: (Start) a(4) has (the following number having 154 decimal digits) 80723047260282253793826303970853990300713679217387 \ 43031867082828418414481568309149198911814701229483 \ 451981557574771156496457238535299087481244990261351117 decimal digits. a(4) = 4^4^4^4 = 4^ 13407807929942597099574024998205846127479365820592 \ 39337772356144372176403007354697680187429816690342 \ 7690031858186486050853753882811946569946433649006084096, the exponent of 4 having 155 decimal digits. (End) The fractional part of 4^4^4*log[10](4) starts .373100157363599870..., so the first few digits of a(4) are 23610226714597313.... - Robert Israel, Jul 06 2016 LINKS Table of n, a(n) for n=0..3. W. Ackermann, Zum Hilbertschen Aufbau der reellen Zahlen, Math. Ann. 99 (1928), 118-133, DOI:10.1007/BF01459088. Eric Weisstein's World of Mathematics, Ackermann Number Wikipedia, Knuth's up-arrow notation MAPLE b:= (n, i)-> `if`(i=0, 1, n^b(n, i-1)): a:= n-> b(n, n): seq(a(n), n=0..3); # Alois P. Heinz, Aug 22 2017 MATHEMATICA a[n_] := If[n == 0, 1, Nest[n^#&, n, n-1]]; Table[a[n], {n, 0, 3}] (* Jean-François Alcover, Mar 19 2019 *) CROSSREFS Cf. A027747, A008868 (which mentions an older estimate for the same number), A266200. Main diagonal of A321312. Sequence in context: A147876 A164796 A324441 * A266200 A066546 A132653 Adjacent sequences: A004228 A004229 A004230 * A004232 A004233 A004234 KEYWORD nonn AUTHOR Daniel Wild (wild(AT)edumath.u-strasbg.fr) STATUS approved

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

Last modified September 17 18:03 EDT 2024. Contains 375990 sequences. (Running on oeis4.)