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A256091 Numbers D such that D^2 = A^3 + B^4 + C^5 for some positive integers A, B, C.

%I A256091 #21 Jan 14 2016 05:09:17
%S A256091 5,7,9,11,17,23,25,33,38,45,55,72,79,89,95,96,99,100,103,105,117,133,
%T A256091 137,163,171,213,218,220,237,239,240,248,255,257,282,303,305,320,347,
%U A256091 355,362,375,384,393,407,408,411,459,475,503,506,513,525,539,540,567,581,613,616,657,659,660,751,752,761,792,796,808,824,833
%N A256091 Numbers D such that D^2 = A^3 + B^4 + C^5 for some positive integers A, B, C.
%C A256091 (8^n*(4^n+8); n = 0, 1, 2, ...) is an infinite subsequence of the subsequence A256613: see that entry for more details.
%H A256091 Chai Wah Wu, <a href="/A256091/b256091.txt">Table of n, a(n) for n = 1..10000</a>
%e A256091 (A, B, C) = (1, 4, 2): 1^3 + 4^4 + 2^5 = 1 + 256 + 32 = 289 = 17^2, so 17 is a term.
%o A256091 (PARI) for(D=3,9999,for(C=1,sqrtn(D^2-2,5),for(B=1,sqrtn(D^2-C^5-1,4),ispower(D^2-C^5-B^4,3)&&print1(D","))))
%o A256091 (PARI) for(D=3, 9999, ok = 0; for(C=1, sqrtn(D^2-2, 5), for(B=1, sqrtn(D^2-C^5-1, 4), ispower(D^2-C^5-B^4, 3)&&(ok=1)&&print1(D", "); if (ok, break)); if (ok, break))) \\ _Michel Marcus_, Apr 26 2015
%Y A256091 Cf. A180241, A180242, A256613, A255830.
%K A256091 nonn
%O A256091 1,1
%A A256091 _M. F. Hasler_, Apr 04 2015
%E A256091 Inserted a(5)=17 and removed the doublet 525 by _Lars Blomberg_, Apr 26 2015