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%I #16 Nov 09 2018 18:22:18
%S 2,17,33,48,82,113,244,257,259,288,324,499,626,657,868,1025,1040,1105,
%T 1280,1297,1328,1539,1649,2320,2402,2433,2644,3126,3141,3206,3381,
%U 3425,3750,4097,4128,4339,4421,5120,5526,6562,6593,6804,7221,7585,7777,7792
%N Numbers of the form a^5 + b^4 with a, b > 0.
%C In view of computing A300566, it would be interesting to have an efficient way to check whether a given (large) n is in this sequence. - _M. F. Hasler_, Apr 25 2018
%t lst={}; Do[p=a^5+b^4; If[p<15000, AppendTo[lst, p]], {a, 16}, {b, 32}]; Union[lst]
%o (PARI) A100294_vec(L=10^6, k=4, m=5, 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. - _M. F. Hasler_, Apr 25 2018
%o (PARI) is(n, k=4, m=5)=for(a=1, sqrtnint(n-1, m), ispower(n-a^m,k) && return(a)) \\ Returns a > 0 if n is in the sequence, or 0 otherwise. - _M. F. Hasler_, Apr 25 2018
%Y Cf. A100274 (primes of the form a^5 + b^4).
%Y Subsequence of A100292 (a^5 + b^2); see also A055394 (a^2 + b^3), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100293 (a^5 + b^3), A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).
%Y Roots of 6th powers are listed in A300566 (z such that z^6 = x^5 + y^4 for some x, y >= 1); see also A300564 (z^4 = x^3 + y^2) and A242183, A300565 (z^5 = x^4 + y^3), A300567 (z^7 = x^6 + y^5), A302174.
%K nonn
%O 1,1
%A _T. D. Noe_, Nov 18 2004
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