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A213619 Let m be the n-th hyperoperation applied to n (see A189896). a(n) is the m-th hyperoperation applied to n and m. 1
1, 2, 65536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let bn=A189896(n), that is bn=H_n(n,n), where H_n is the n-th hyperoperation.

Then

a(n) = H_bn(n,bn), hence

a(0) = H_b0(0,b0) = H_1(0,1) = 0+1 = 1,

a(1) = H_b1(1,b1) = H_2(1,2) = 1*2 = 2,

a(2) = H_b2(2,b2) = H_4(2,4) = 2^2^2^2 = 65536, and

a(3) is too large.

LINKS

Table of n, a(n) for n=0..2.

FORMULA

a(n) = H_H_n(n,n)(n,H(n,n)).

EXAMPLE

a(0) = H_H_0(0,0)(0,H_0(0,0)) = H_1(0,1) = 0+1 = 1.

a(1) = H_H_1(1,1)(1,H_1(1,1)) = H_2(1,1+1) = 1*(1+1) = 2.

a(2) = H_H_2(2,2)(2,H_2(2,2)) = H_4(2,2*2) = H_3(2,H_3(2,H_3(2,2))) = 2^2^2^2 = 2^2^4 = 2^16 = 65536.

CROSSREFS

Cf. A189896.

Sequence in context: A306907 A052427 A051833 * A060895 A100266 A272137

Adjacent sequences:  A213616 A213617 A213618 * A213620 A213621 A213622

KEYWORD

nonn,bref

AUTHOR

Jens Ahlström, Jun 16 2012

STATUS

approved

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Last modified April 9 10:32 EDT 2020. Contains 333348 sequences. (Running on oeis4.)