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%I #24 Feb 02 2016 03:35:47
%S 5,9,12,17,19,21,23,25,28,33,35,37,38,39,42,45,46,47,51,53,55,57,59,
%T 60,61,65,66,67,68,69,70,71,72,73,75,77,80,81,82,84,87,88,89,91,93,95,
%U 97,98,99,100,103,105,107,108,109,110,111,112,113,114,115,116,117,118,119,121,123,124,127,128,129,131,132,133,134,135,136,139,141
%N Numbers D such that D^2 = A^2 + B^3 + C^4 has more than one solution in positive integers (A, B, C).
%C The subsequence of terms of A180241 whose square has more than one representation of the given form. See A256603 and A256652 are the analog for A256091 and A255830.
%H Chai Wah Wu, <a href="/A256604/b256604.txt">Table of n, a(n) for n = 1..10088</a>
%e (A, B, C) = (4, 8, 1): 4^2 + 8^3 + 1^4 = 16 + 512 + 1 = 529 = 23^2 and
%e (A, B, C) = (1, 8, 2): 1^2 + 8^3 + 2^4 = 1 + 512 + 16 = 529 = 23^2,
%e so 23 is a term.
%o (PARI) for(D=2,199,my(f=-1,B,D2C4);for(C=1,sqrtint(D),D2C4=D^2-C^4; B=0;while(B++^3<D2C4,issquare(D2C4-B^3)&&f++&print1(D",")+next(3)))) \\ Converted to integer arithmetic by _M. F. Hasler_, May 01 2015
%Y Cf. A180241, A180242, A256613, A255830.
%K nonn
%O 1,1
%A _M. F. Hasler_, Apr 06 2015
%E Inserted a(7)=23 by _Lars Blomberg_, Apr 26 2015