• Maple's magical bounds break even the simplest tasks.

    From [email protected]@21:1/5 to All on Fri May 12 13:33:16 2023
    With Maple 2023.0:

    a := n -> denom(add((n-j)/j, j=1..n)):
    b := n -> denom(n*harmonic(n)):

    seq(a(n), n = 1..13);
    seq(b(n), n = 1..13);

    1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720
    1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720

    seq(print([n, a(n)]), n=599..600);
    seq(print([n, b(n)]), n=599..600);

    [599, 24518...43033600]
    [600, 44775...38628544]

    [599, 1]
    [600, 1]

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  • From Nasser M. Abbasi@21:1/5 to [email protected] on Sat May 13 21:17:38 2023
    On 5/12/2023 3:33 PM, [email protected] wrote:
    With Maple 2023.0:

    a := n -> denom(add((n-j)/j, j=1..n)):
    b := n -> denom(n*harmonic(n)):

    seq(a(n), n = 1..13);
    seq(b(n), n = 1..13);

    1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720
    1, 1, 2, 3, 12, 10, 20, 35, 280, 252, 2520, 2310, 27720

    seq(print([n, a(n)]), n=599..600);
    seq(print([n, b(n)]), n=599..600);

    [599, 24518...43033600]
    [600, 44775...38628544]

    [599, 1]
    [600, 1]


    a(n) is not the same as b(n) for large n. They give different
    results starting at n=501.

    b := n -> denom(n*harmonic(n)):
    a := n -> denom(add((n-j)/j, j=1..n)):

    b(501)
    1
    a(501)
    1949158278614846....34240

    So if you limit the print to n=500, it works

    seq(lprint([n, b(n)]), n=499..500);
    [499, 4892426340611412598120499299869225038728212308035354645714708753146045919\
    8933676282116072023975502328168545495423118821451779568011772436268745785346466\
    134503715040454880025595359981443379389168637406283325898144000]
    [500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
    0535808929551839879927551323512208404432272583808876008875748891396208293775773\
    202234707610373970265544169261480492630390300131470759246347712]


    seq(lprint([n, a(n)]), n=499..500);
    [499, 4892426340611412598120499299869225038728212308035354645714708753146045919\
    8933676282116072023975502328168545495423118821451779568011772436268745785346466\
    134503715040454880025595359981443379389168637406283325898144000]
    [500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
    0535808929551839879927551323512208404432272583808876008875748891396208293775773\
    202234707610373970265544169261480492630390300131470759246347712]


    Now

    seq(lprint([n, b(n)]), n=500..501);
    [500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
    0535808929551839879927551323512208404432272583808876008875748891396208293775773\
    202234707610373970265544169261480492630390300131470759246347712]
    [501, 1]


    seq(lprint([n, a(n)]), n=500..501);
    [500, 4882641487930189772924258301269486588650755883419283936423279335639753828\
    0535808929551839879927551323512208404432272583808876008875748891396208293775773\
    202234707610373970265544169261480492630390300131470759246347712]
    [501, 1949158278614846216736230858790214207046209933500712150268774185884133264\
    6920482606607520910150719091222438484803302428666217967615069417723037243024260\
    75937513277859240329961843084290638428358894216825180009834240]


    Are these supposed to give same result for any n, no matter how
    large it is?

    --Nasser

    --Nasser

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