The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A189896

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A189896

Weak Ackermann numbers: H_n(n,n) where H_n is the n-th hyperoperator.
(history; published version)

#75 by Michael De Vlieger at Tue Nov 15 17:51:53 EST 2022

STATUS

proposed

approved

#74 by Charles R Greathouse IV at Tue Nov 15 15:48:23 EST 2022

STATUS

editing

proposed

#73 by Charles R Greathouse IV at Tue Nov 15 15:47:26 EST 2022

COMMENTS

The next term, a(4), would have approximately 5.4 has about 8* 10^307 153 decimal digits. - _M. F. Hasler_, Jun 17 2012Charles R Greathouse IV_, Nov 15 2022

STATUS

approved

editing

#72 by N. J. A. Sloane at Sat Jan 11 15:57:46 EST 2020

CROSSREFS

Cf. A271553 ( H_n-1(n,n) ). - _Natan Arie' Consigli_, Apr 10 2016

EXTENSIONS

"Weak" added to definition by _Natan Arie' Consigli_, Apr 18 2015

Discussion

Sat Jan 11

15:57

OEIS Server: https://oeis.org/edit/global/2842

#71 by Alois P. Heinz at Thu Dec 21 07:26:07 EST 2017

STATUS

reviewed

approved

#70 by Michel Marcus at Thu Dec 21 04:31:45 EST 2017

STATUS

proposed

reviewed

#69 by Jon E. Schoenfield at Sat Dec 16 16:04:48 EST 2017

STATUS

editing

proposed

Discussion

Mon Dec 18

05:27

Bruno Curfs: OK. I agree. I was taken aback by the "odd" numbers being used and the change of base from 4 to 2. I wanted it to be this log_4(4^4^4^4) = 2^512, but didn't realize that the original was correct. My apology.

19:54

Jon E. Schoenfield: No problem!  :-)

#68 by Jon E. Schoenfield at Sat Dec 16 15:59:19 EST 2017

EXAMPLE

a(4) = 4^4^4^4 = 4^(4^(4^4)) = 4^(4^256), because the fourth hyperoperation is tetration. The term is too big to be included: log_42(a(4)) = 2^512513.

Discussion

Sat Dec 16

16:04

Jon E. Schoenfield: The original statement that log_2(a(4)) = 2^513 was correct:  log_2(a(4)) = log_2(4^(4^(4^4))) = log_2((2^2)^(4^(4^4))) = log_2(2^(2*4^(4^4))) = 2*4^(4^4)) = 2*4^256 = 2*4^256 = 2*2^512 = 2^513.

#67 by Jon E. Schoenfield at Sat Dec 16 15:54:45 EST 2017

EXAMPLE

a(4) = 4^4^4^4 = 4^(4^(4^4) ) = 4^(4^256), because the fourth hyperoperation is tetration. The term is too big to be included: log_4(a(4)) = 2^513512.

STATUS

proposed

editing

#66 by Bruno Curfs at Fri Dec 15 20:05:37 EST 2017

STATUS

editing

proposed