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A264901
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Sorted powers C^z = A^x + B^y with all positive integers and x,y,z > 2, with multiplicity.
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4
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16, 32, 64, 64, 128, 128, 128, 243, 256, 256, 512, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024, 2048, 2048, 2048, 2744, 4096, 4096, 4096, 4096, 6561, 6561, 6561, 6561, 8192, 8192, 8192, 8192, 8192, 8192
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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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
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EXAMPLE
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128 = 64 + 64 ==> 2^7 = 2^6 + 2^6 = 2^6 + 4^3 = 4^3 + 4^3 (but not 4^3 + 2^6).
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PROG
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(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); }
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CROSSREFS
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Cf. A245713, A261782.
Sequence in context: A204645 A236323 A018923 * A339840 A172418 A036967
Adjacent sequences: A264898 A264899 A264900 * A264902 A264903 A264904
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KEYWORD
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nonn,easy
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AUTHOR
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Anatoly E. Voevudko, Nov 28 2015
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STATUS
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approved
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