OFFSET
1,1
COMMENTS
Based on an observation of Ed Pegg Jr, who supplied terms a(2)-a(6) and a(8).
LINKS
Joerg Arndt and Donovan Johnson, Table of n, a(n) for n = 1..300 (first 55 terms from Joerg Arndt)
EXAMPLE
228 is in the sequence because 228^2 = 11^3 + 37^3 and gcd(11, 37) = 1.
MATHEMATICA
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 *)
PROG
(PARI)
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 */
(PARI)
/* 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 */
(PARI) 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
CROSSREFS
KEYWORD
nonn
AUTHOR
Hans Havermann, Oct 15 2004
EXTENSIONS
More terms from Hans Havermann and Bodo Zinser, Oct 20 2004
STATUS
approved