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  • Rpakr

    In this blog post, I explain how the last digit of fish number 1, fish number 2 and fish number 3 can be calculated.


    Definition of fish number 1 is complex, but it is actually just iterated Ackermann function. Let \(A(n)=Ack(n,n)\) in Ackermann function. Fish number is \(A^n(3)\) with some natural number \(n\). \(Ack(m,n)=2\uparrow^{m-2}(n+3)-3\) so \(A(n)=2\uparrow^{n-2}(n+3)-3=(2\uparrow\uparrow a)-3\) for \(n>3\). First we have to find \(2^n mod10\). \(2^1=2\equiv2 mod10\) \(2^2=4\equiv4 mod10\) \(2^3=8\equiv8 mod10\) \(2^4=16\equiv6 mod10\) \(2^5=32\equiv2 mod10 \cdots\)

    \(2^{4k+1}\equiv2 mod10\) \(2^{4k+2}\equiv4 mod10\) \(2^{4k+3}\equiv8 mod10\) \(2^{4k+4}\equiv6 mod10\)

    So \(2^n mod 10\) has a cycle 2,4,8,6,2,4,8,6,2,4,8,6,...

    Then we …


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  • Rpakr

    The formulas for 1.0-1.2 seems to be wrong, so it's corrected to 250x^2+250x+10.

    His formulas can be found here .

    PsiCubed2's fractional Psi Levels can be found here .



    n \(\psi(n)\)
    0 0
    0.01 0.1
    0.02 0.2
    0.03 0.3
    0.04 0.4
    0.05 0.5
    0.06 0.6
    0.07 0.7
    0.08 0.8
    0.09 0.9
    0.1 1
    0.11 1.1
    0.12 1.2
    0.13 1.3
    0.14 1.4
    0.15 1.5
    0.16 1.6
    0.17 1.7
    0.18 1.8
    0.19 1.9
    0.2 2
    0.21 2.1
    0.22 2.2
    0.23 2.3
    0.24 2.4
    0.25 2.5
    0.26 2.6
    0.27 2.7
    0.28 2.8
    0.29 2.9
    0.3 3
    0.31 3.1
    0.32 3.2
    0.33 3.3
    0.34 3.4
    0.35 3.5
    0.36 3.6
    0.37 3.7
    0.38 3.8
    0.39 3.9
    0.4 4
    0.41 4.1
    0.42 4.2
    0.43 4.3
    0.44 4.4
    0.45 4.5
    0.46 4.6
    0.47 4.7
    0.48 4.8
    0.49 4.9
    0.5 5
    0.51 5.1
    0.52 5.2
    0.53 5.3
    0.54 5.4
    0.55 5.5
    0.56 5.6
    0.57 5.7
    0.58 5.8
    0.59 5.9
    0.6 6
    0.61 6.1
    0.62 6.2
    0.63 6.3
    0.64 6.4
    0.65 6.5
    0.66 6.6
    0.67 6.7
    0.68 6.8
    0.69 6.9
    0.7 7
    0.71 7.1
    0.72 7.2
    0.73 7.3
    0.74 7.4
    0.75 …













































































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  • Rpakr

    Name Notation Numbers FGH Level
    1 Guppy regiment E# 504 \(2\)
    2 Grangol regiment 188 \(3\)
    3 Greagol regiment 76 \(4\)
    4 Gigangol regiment 59 \(5\)
    5 Gorgegol regiment 53 \(6\)
    6 Gulgol regiment 48 \(7\)
    7 Gaspgol regiment 46 \(8\)
    8 Ginorgol regiment 43 \(9\)
    9 Gargantuul regiment 47 \(10\)
    10 Googondol regiment 77 \(11\)
    11 Gugold regiment xE# 13 \(\omega\)
    12 Graatagold regiment 13 \(\omega+1\)
    13 Greegold regiment 13 \(\omega+2\)
    14 Grinningold regiment 13 \(\omega+3\)
    15 Golaagold regiment 13 \(\omega+4\)
    16 Gruelohgold regiment 13 \(\omega+5\)
    17 Gaspgold regiment 13 \(\omega+6\)
    18 Ginorgold regiment 13 \(\omega+7\)
    19 Gargantuuld regiment 13 \(\omega+8\)
    20 Googondold regiment 41 \(\omega+9\)
    21 Gugolthra regiment 286 \(\omega\times2\)
    22 Throogol regim…






















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  • Rpakr

    Value of 2↑↑5

    August 3, 2017 by Rpakr

    Source: https://apfloat.appspot.com/

    20035299304068464649790723515602557504478254755697514192650169737108940595563114530895061308809333481010382343429072631818229493821188126688695063647615470291650418719163515879663472194429309279820843091048559905701593189596395248633723672030029169695921561087649488892540908059114570376752085002066715637023661263597471448071117748158809141357427209671901518362825606180914588526998261414250301233911082736038437678764490432059603791244909057075603140350761625624760318637931264847037437829549756137709816046144133086921181024859591523801953310302921628001605686701056516467505680387415294638422448452925373614425336143737290883037946012747249584148649159306472520151556939226281806916507963810641322753072671439…

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  • Rpakr

    Number Value
    Million Read more >