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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
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
KEYWORD
nonn,bref
AUTHOR
STATUS
approved

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