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A175796 H_n(n, 2) where H_c(a, b) is the hyperoperation function with operator c. 1
3, 3, 4, 9, 256 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..4.

Wikipedia, Hyperoperation

Index Section Ho-Hy

FORMULA

a(n) = H_n(n, 2)

H_c(a, b) = {b + 1 if c = 0; a if c = 1, b = 0; 0 if c = 2, b = 0; 1 if c >= 3, b = 0; H_{c-1}(a, H_c(a, b - 1)) otherwise}

EXAMPLE

a(0) = H_0(0, 2) = 2 + 1 = 3

a(1) = H_1(1, 2) = 1 + 2 = 3

a(2) = H_2(2, 2) = 2 * 2 = 4

a(3) = H_3(3, 2) = 3 ^ 2 = 9

a(4) = H_4(4, 2) = 4 ^^ 2 = 4 ^ 4 = 256

a(5) = H_5(5, 2) = 5 ^^^ 2 = 5 ^^ 5 = 5 ^ 5 ^ 5 ^ 5 ^ 5 =~ 10 ^ (10 ^ (10 ^ (2184.1257...)))

PROG

(Python) def H(a, b, c):

..if c == 0: return b + 1

..if c == 1 and b == 0: return a

..if c == 2 and b == 0: return 0

..if c >= 3 and b == 0: return 1

..return H(a, H(a, b - 1, c), c - 1)

for n in range(5): print H(n, 2, n)

CROSSREFS

For H_n(x,2) with fixed x, cf. A054871 (x=3), A253855 (x=4), A255176 (x=2), A256131 (x=10), A261143 (x=1). - Danny Rorabaugh, Oct 20 2015

Sequence in context: A107635 A132319 A130626 * A115284 A202869 A202871

Adjacent sequences:  A175793 A175794 A175795 * A175797 A175798 A175799

KEYWORD

nonn

AUTHOR

Grant Garcia, Sep 06 2010

STATUS

approved

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Last modified July 11 18:19 EDT 2020. Contains 335652 sequences. (Running on oeis4.)