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A264901 Sorted powers C^z = A^x + B^y with all positive integers and x,y,z > 2, with multiplicity. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A204645 A236323 A018923 * A339840 A172418 A369170
KEYWORD
nonn,easy
AUTHOR
Anatoly E. Voevudko, Nov 28 2015
STATUS
approved

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Last modified June 25 10:55 EDT 2024. Contains 373701 sequences. (Running on oeis4.)