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%I #5 May 05 2018 02:21:18
%S 2,129,257,384,2188,2443,6562,6689,8748,16385,16640,22945,65537,65664,
%T 67723,78126,78381,81920,84686,143661,279937,280192,286497,345472,
%U 390626,390753,392812,407009,468750,670561,823544,823799,830104,889079,1214168,1679617,1679744,1681803
%N Numbers of the form a^7 + b^8, with integers a, b > 0.
%C Although it is easy to produce many terms of this sequence, it is nontrivial to check efficiently whether a very large number is of this form.
%e The sequence starts with 1^7 + 1^8, 2^7 + 1^8, 1^7 + 2^8, 2^7 + 2^8, 3^7 + 1^8, 3^7 + 2^8, 1^7 + 3^8, 2^7 + 3^8, 3^7 + 3^8, 4^7 + 1^8, 4^7 + 2^8, 4^7 + 3^8, 1, ...
%t With[{nn=40}, Take[Union[First[#]^7 + Last[#]^8&/@Tuples[Range[nn], 2]], nn]]
%o (PARI) is(n,k=7,m=8)=for(b=1,sqrtnint(n-1,m),ispower(n-b^m,n)&&return(b)) \\ Returns b > 0 if n is in the sequence, else 0.
%o A303377_vec(L=10^7,k=7,m=8,S=List())={for(a=1,sqrtnint(L-1,m),for(b=1,sqrtnint(L-a^m,k), listput(S,a^m+b^k)));Set(S)} \\ all terms up to limit L
%Y Cf. A000404 (a^2 + b^2), A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4).
%Y Cf. A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6), A303376 (a^6 + b^7).
%K nonn,easy
%O 1,1
%A _M. F. Hasler_, May 04 2018
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