This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
3 = 1^6 + 1^6 + 1^6; 857 = 2^6 + 2^6 + 3^6; 1459 = 1^6 + 3^6 + 3^6, etc.
N:= 10^8: # to get all terms <= N
S:= [seq(i^6, i=1..floor(N^(1/6)))]:
S3:= {seq(seq(seq(S[i]+S[j]+S[k],k=1..j),j=1..i),i=1..nops(S))}:
sort(convert(select(t -> t <= N and isprime(t), S3), list)); # Robert Israel, Mar 09 2017
nn = 15; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^6)], # <= nn^6 && PrimeQ[#] &]
list(lim)=my(v=List(),a6,a6b6,t); lim\=1; for(a=1,sqrtnint(lim-2,6), a6=a^6; for(b=1,min(sqrtnint(lim-a6-1,6),a), a6b6=a6+b^6; forstep(c=if(a6b6%2,2,1),min(sqrtnint(lim-a6b6,6),b),2, if(isprime(t=a6b6+c^6), listput(v,t))))); Set(v) \\ Charles R Greathouse IV, Mar 09 2017
3 = 1^7 + 1^7 + 1^7; 257 = 1^7 + 2^7 + 2^7; 82499 = 3^7 + 3^7 + 5^7, etc.
N:= 10^9: # to get all terms <= N
Res:= {}:
for x from 1 to floor(N^(1/7)) do
for y from 1 to min(x, floor((N-x^7)^(1/7))) do
for z from 1 to min(y, floor((N-x^7-y^7)^(1/7))) do
p:= x^7 + y^7 + z^7;
if isprime(p) then Res:= Res union {p} fi
od od od:
sort(convert(Res,list)); # Robert Israel, Feb 26 2017
nn = 14; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^7)], # <= nn^7 && PrimeQ[#] &]
list(lim)=my(v=List(),x7,y7,t,p); for(x=1,sqrtnint(lim\3,7), x7=x^7; for(y=x,sqrtnint((lim-x7)\2,7), y7=y^7; t=x7+y7; forstep(z=y+(x+1)%2,sqrtnint((lim-t)\1,7),2, if(isprime(p=t+z^7), listput(v,p))))); Set(v) \\ Charles R Greathouse IV, Feb 27 2017
3 = 1^8 + 1^8 + 1^8; 6563 = 1^8 + 1^8 + 3^8; 72353 = 2^8 + 3^8 + 4^8, etc.
nn = 13; Select[Union[Plus @@@ (Tuples[Range[nn], {3}]^8)], # <= nn^8 && PrimeQ[#] &]
list(lim)=my(v=List(),A,B,t); lim\=1; for(a=1,sqrtnint(lim-2,8), A=a^8; for(b=1,min(sqrtnint(lim-A-1,8),a), B=A+b^8; forstep(c=if(B%2,2,1),sqrtnint(lim-B,8),2, if(isprime(t=B+c^8), listput(v,t))))); Set(v) \\ Charles R Greathouse IV, Nov 05 2017
9043=6^5+4^5+3^5. 17863=7^5+4^5+2^5. 32801=8^5+2^5+1^5. 40787=8^5+6^5+3^5, 43669=8^5+6^5+5^5.
lst={};Do[Do[Do[p=n^5+m^5+k^5;If[PrimeQ[p],AppendTo[lst,p]],{n,m+1,3*4!}], {m,k+1,6!}],{k,2*6!}];Take[Union[lst],5! ]
Module[{upto=10^6},Select[Total/@Subsets[Range[Ceiling[Surd[upto,5]]]^5,{3}], PrimeQ[#]&&#<=upto&]]//Union (* Harvey P. Dale, May 01 2019 *)
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