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 A173566 a(n+1) = a(n)^a(n), with a(1) = 2. 1
 2, 4, 256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The next term, a(4), is 2^2048, with 617 digits. From Natan Arie Consigli, Dec 01 2015: (Start) Possible other sequence with the same first three entries: a(1) = 2; a(2) = Triangle(2); a(3) = Square(2); a(4) = Pentagon(2); etc., where, in Steinhaus-Moser notation, Triangle(n) = n^n; Square(n) = Triangle(Triangle...(n)...) (with n inside n nested triangles); Pentagon(n) = Square(Square...(n)...)(with n inside n nested squares); etc. Start with a(1) = 2, a(2) = triangle(2) = 4, a(3) = square(2) = 256, a(4) = pentagon(4) = 256^^256 (power tower of 256s with height 256). (End) LINKS Michel Marcus, Table of n, a(n) for n = 1..4 Wikipedia, Steinhaus-Moser notation. EXAMPLE a(3) = square(2) = triangle(triangle(2)) = triangle(2^2) = 4^4 = 256. MATHEMATICA RecurrenceTable[{a[1] == 2, a[n] == a[n - 1]^a[n - 1]}, a, {n, 4}] (* Vincenzo Librandi, Dec 17 2015 *) PROG (Magma) [n le 1 select 2 else Self(n-1)^Self(n-1): n in [1..4]]; // Vincenzo Librandi, Dec 17 2015 CROSSREFS Cf. A030798 ("preceding term"), A054874 (log base 2). Sequence in context: A009673 A018770 A260755 * A271551 A058990 A343255 Adjacent sequences: A173563 A173564 A173565 * A173567 A173568 A173569 KEYWORD nonn,bref AUTHOR Franklin T. Adams-Watters, Aug 03 2011 STATUS approved

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Last modified April 20 16:37 EDT 2024. Contains 371845 sequences. (Running on oeis4.)