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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 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 Cf. A245713, A261782. Sequence in context: A204645 A236323 A018923 * A339840 A172418 A036967 Adjacent sequences:  A264898 A264899 A264900 * A264902 A264903 A264904 KEYWORD nonn,easy AUTHOR Anatoly E. Voevudko, Nov 28 2015 STATUS approved

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Last modified April 13 19:02 EDT 2021. Contains 342939 sequences. (Running on oeis4.)