A156668 -id:A156668 - cp's OEIS frontend

A186082 Numbers k such that log(A156668(k)*(1 + k mod 2))/k^2 is smaller than for any prior k.

1, 2, 3, 5, 10, 13, 18, 31, 49, 98, 116, 232, 281, 397, 678, 1075, 2150, 3225, 4300, 5375, 5772, 6847, 7922, 8997, 17994, 19069

Offset: 1

Kevin T. Acres, Feb 12 2011

			[1,  0.6931471805599453094172321215]
[2,  0.5994738181995926360154858945]
[3,  0.5898075219334671955890478209]
[5,  0.5866039232314788114510488867]
[10, 0.5865963134453746145925657102]
[13, 0.5864356249925781873672553233]
[18, 0.5864232678262123920533476064]

David Broadhurst, Table of n for n = 1..1000
Kevin Acres and David Broadhurst, Rational points on y^2 = x^3 + 10*x^2 + 5*x

Cf. A156668.

T(k)={
    local(P=ellpow(ellinit([0,10,0,5,0]),[-1,2],k),s,t);
    s=P[1]^2;
    t=abs(numerator(P[2]^4/s-80*s));
    while(t%2==0,t=t/2;);
    t;
}
M(k)=1+k%2;
V(k)=log(M(k)*T(k))/k^2;
{
    lowest=1;
    for(i=1,20000,
        l=V(i);
        if(l

A156669 Positive integers k such that k^2 = (m^5 + n^5)/(m + n) for some nonnegative coprime integers m, n.

Original entry on oeis.org

1, 101, 13361, 1612186411, 1624763543401, 240020196429554642201, 29891946989942513908518251, 5506336596007252456855684531229391026385301, 92724987584857206382605250844078768507060135044811

Offset: 1

Max Alekseyev, Feb 13 2009

nonn

			13361 belongs to this sequence since 13361^2 = (35^5 + 123^5) / (35 + 123) with gcd(35, 123) = 1.

Cf. A156668, A156670.

A156670 Positive integers k such that k^2 = (m^5 - n^5)/(m - n) for some nonnegative coprime integers m, n.

Original entry on oeis.org

1, 11, 1169341, 20188985439712961, 3506790234728288196345900732301, 5190947078637547438603476743093680561, 1041849413143039115171399776907273433339109867252078165841

Offset: 1

Max Alekseyev, Feb 13 2009

nonn

			1169341 belongs to this sequence since 1169341^2 = (808^5 - 627^5) / (808 - 627) with gcd(808, 627) = 1.

Cf. A156668, A156669.

cp's OEIS Frontend

A186082 Numbers k such that log(A156668(k)*(1 + k mod 2))/k^2 is smaller than for any prior k.

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A156669 Positive integers k such that k^2 = (m^5 + n^5)/(m + n) for some nonnegative coprime integers m, n.

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Crossrefs

A156670 Positive integers k such that k^2 = (m^5 - n^5)/(m - n) for some nonnegative coprime integers m, n.

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Author

Keywords

Examples

Crossrefs