A099532 -id:A099532 - cp's OEIS frontend

A099533 Greater of a,b where n^2 = a^3 + b^3; a,b>0 and gcd(a,b)=1. The lesser of a,b is the corresponding term in A099532 and n, which is used to order this sequence, is the corresponding term in A099426.

2, 37, 65, 112, 312, 433, 1064, 877, 1177, 1201, 1617, 1969, 2345, 2480, 2543, 3081, 3482, 4019, 4440, 5160, 6337, 6489, 5985, 7729, 8663, 9265, 10274, 8848, 10753, 12688, 11821, 12071, 14345, 13937, 16352, 15520, 17761, 16296, 15962, 21923

Offset: 1

Hans Havermann, Oct 20 2004

nonn

			Term #2 is 37 because term #2 of A099426 is 228, 228^2 = 11^3 + 37^3 and 37 > 11.

Donovan Johnson, Table of n, a(n) for n = 1..300

Cf. A099426, A099532, A282639 (sorted not by n but max(a,b)).

for(s=2,1e5,for(x=1,s\2,my(y=s-x);if(gcd(x,y)>1,next); if(issquare(x^3+y^3), print1(y", ")))) \\ Charles R Greathouse IV, Nov 06 2014

A099426 Numbers n where n^2 = x^3 + y^3; x,y>0 and gcd(x,y)=1.

Original entry on oeis.org

3, 228, 671, 1261, 6371, 9765, 35113, 35928, 40380, 41643, 66599, 112245, 124501, 127499, 167160, 191771, 205485, 255720, 297037, 377567, 532392, 546013, 647569, 681285, 812340, 897623, 1043469, 1125683, 1261491, 1431793, 1433040, 1584828, 1783067, 1984009, 2107391, 2372903, 2440893, 2484469, 2548557

Offset: 1

Hans Havermann, Oct 15 2004

nonn

Based on an observation of Ed Pegg Jr, who supplied terms a(2)-a(6) and a(8).

			228 is in the sequence because 228^2 = 11^3 + 37^3 and gcd(11, 37) = 1.

Joerg Arndt and Donovan Johnson, Table of n, a(n) for n = 1..300 (first 55 terms from Joerg Arndt)

Cf. A099532, A099533, A103255 (min(x,y), sorted), A282639 (max(x,y)).

n = 10^7; n2 = n^2; x = 1; x3 = x^3; Reap[ While[x3 < n2, y = x + 1; y3 = y^3; While[y3 < n2, If[GCD[x, y] == 1, s = x3 + y3; If[ IntegerQ[r = Sqrt[s]], Print[r]; Sow[r]; Break[]]]; y += 1; y3 = y^3]; x += 1; x3 = x^3]][[2, 1]] // Sort (* Jean-François Alcover, Jan 11 2013, translated from Joerg Arndt's 2nd Pari program *)

is_A099426(n)=
{
    my(n2=n^2, k=1, k3=1, r);
    while( k3 < n2,
        if ( ispower(n2-k3, 3, &r),
            if ( gcd(r,k)==1, return(1) );
        );
        k+=1;  k3=k^3;
    );
    return(0);
}
for (n=1,10^8, if( is_A099426(n), print1(n,", ")) );
/* Joerg Arndt, Sep 30 2012 */

/* compute all terms below a threshold at once, terms need to be sorted */
{ N = 10^7; N2 = N^2;
x=1; x3=x^3;
while ( x3 < N2,
    y=x+1; y3=y^3;
    while ( y3 < N2,
        if ( gcd(x,y) == 1,
            s = x3 + y3;
            if ( issquare(s, &r), print(r); break(); );
        );
        y+=1;  y3 = y^3;
    );
    x+=1;  x3 = x^3;
);}
/* Joerg Arndt, Sep 30 2012 */

for(s=2,1e5,for(x=1,s\2,my(y=s-x);if(gcd(x,y)>1,next); if(issquare(x^3+y^3), print1(s", ")))) \\ Charles R Greathouse IV, Nov 06 2014

More terms from Hans Havermann and Bodo Zinser, Oct 20 2004

cp's OEIS Frontend

A099533 Greater of a,b where n^2 = a^3 + b^3; a,b>0 and gcd(a,b)=1. The lesser of a,b is the corresponding term in A099532 and n, which is used to order this sequence, is the corresponding term in A099426.

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A099426 Numbers n where n^2 = x^3 + y^3; x,y>0 and gcd(x,y)=1.

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