OFFSET
1,1
COMMENTS
We do not distinguish between the representations C^z = A^x + B^y and C^z = B^y + A^x.
This sequence is based on the type of equation involved in Beal's conjecture.
LINKS
Anatoly E. Voevudko, Table of n, a(n) for n = 1..615
American Mathematical Society, Beal Prize
Anatoly E. Voevudko, Description of all powers in b245713
Anatoly E. Voevudko, Description of all powers in b261782
Anatoly E. Voevudko, Description of all powers in b264901
Wikipedia, Beal's conjecture
EXAMPLE
128 = 64 + 64 ==> 2^7 = 2^6 + 2^6 = 2^6 + 4^3 = 4^3 + 4^3 (but not 4^3 + 2^6).
PROG
(PARI) b264901(lim)=
{my(Lc=List(1), Lb=List(), La=Lb, czn, lan, lbn, lcn, lim2=logint(lim, 2), lim3);
for(z=3, lim2, lim3=sqrtnint(lim, z); for(C=2, lim3, listput(Lc, C^z)));
lcn=#Lc; if(lcn==0, return(-1));
for(i=1, lcn, for(j=i, lcn, czn=Lc[i]+Lc[j]; if(czn>lim, next);
La=findinlista(Lc, czn); lan=#La; if(!lan, next);
for(k=1, lan, listput(Lb, czn)); )); lbn=#Lb; listsort(Lb);
for(i=1, lbn, print(i, " ", Lb[i]))}
findinlista(list, item, sind=1)=
{my(ln=#list, Li=List()); if(ln==0 || sind<1 || sind>ln, return(Li));
for(i=sind, ln, if(list[i]==item, listput(Li, i))); return(Li); }
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Anatoly E. Voevudko, Nov 28 2015
STATUS
approved